Area and perimeter

The space inside and the distance round — and the shared edge that is counted twice by mistake.

print a sheet of all 26 → · the same sheet with answers, for a grown-up

G21-A122 marksSINGA 2021 Assessment — Primary 4 (SMC Practice Book)

The figure is made up of 5 identical squares arranged as a cross of diamonds, each outer square joined to the middle one along a full side. The perimeter of the figure is 132 cm. What is the area of each square?

      /\      /\
     /  \    /  \
    /    \  /    \
    \     \/     /
     \    /\    /
      \  /  \  /
       \/    \/
       /\    /\
      /  \  /  \
     /    \/    \
     \    /\    /
      \  /  \  /
       \/    \/

  5 identical squares · the middle one shares all 4 of its sides
  ⚠ the drawing above does NOT show this — go by the words, not the picture

answer, method and trap →

G21-A172 marksSINGA 2021 Assessment — Primary 4 (SMC Practice Book)

In the diagram, ABEF is a square and BCDE is a rectangle. The length of AF is twice the length of BC and AB = 56 cm. Find the length of ED.

  A                    B         C
  +--------------------+---------+
  |                    |        /|
  |      square        |  rect / |
  |      ABEF          |      /  |
  +--------------------+---------+
  F                    E         D

  AB = 56 cm · AF = 2 x BC

answer, method and trap →

G21-A262 marksSINGA 2021 Assessment — Primary 4 (SMC Practice Book)

A rectangular piece of paper is folded as shown below, with both top corners folded down. The flat top that is left is 7 cm across, each folded corner covers 6 cm, and the height of the figure is 23 cm. What is the area of the piece of paper at first?

  - - - - - +-------------+ - - - - -   -+
  |        /|   7 cm      |\        |     |
  |      /  |             |  \      |     |
  +----/----+-------------+----\----+     |
  |<-6cm->|               |<-6cm->|     23 cm
  |                                 |     |
  |                                 |     |
  |                                 |     |
  +---------------------------------+    -+

  the dashed lines show where the corners came from

answer, method and trap →

G21-A292 marksSINGA 2021 Assessment — Primary 4 (SMC Practice Book)

ABCD is a square of side 8 cm, cut out of a 28 cm by 12 cm rectangle. What is the area of the shaded part (the rectangle outside the square)?

  |<----------------- 28 cm ----------------->|
  +###########################################+  -+
  ###########+-----------+#####################   |
  ###########|  A     B  |#####################   |
  ###########|   8 cm    |##################### 12 cm
  ###########|  D     C  |#####################   |
  ###########+-----------+#####################   |
  +###########################################+  -+

answer, method and trap →

G21-A302 marksSINGA 2021 Assessment — Primary 4 (SMC Practice Book)
The figures show a square and a rectangle. Square X has sides of 10 cm. Rectangle Y is 2 cm wide. The area of Square X is 4 times the area of Rectangle Y. Find the perimeter of Rectangle Y.
```
     Square X            Rectangle Y
   +----------+            +--+
   |          |            |  |
   |  10 cm   |            |  |  2 cm wide
   |          |            |  |
   +----------+            +--+
```
answer, method and trap →
G21-A312 marksSINGA 2021 Assessment — Primary 4 (SMC Practice Book)
Find the perimeter of the I-shaped figure below. All lines meet at right angles. The figure is 14 cm across and 16 cm tall; the top and bottom bars are each 5 cm deep, and the waist is set in 3 cm on the left and 4 cm on the right.
```
  |<-------- 14 cm -------->|
  +-------------------------+  -+
  |                         |   | 5 cm
  +----+---------------+----+  -+
  |3cm |               | 4cm|
       |               |         16 cm
  +----+---------------+----+
  |                         |   | 5 cm
  +-------------------------+  -+
```
answer, method and trap →
G21-A382 marksSINGA 2021 Assessment — Primary 4 (SMC Practice Book)
The figure is made up of 4 identical rectangles: two standing upright side by side (22 cm tall, 14 cm across the pair) resting centrally on two more lying end to end to form the base. Find the length of XY, the part of the base sticking out to the right of the upright pair.
```
        |<- 14 cm ->|
        +-----+-----+   -+
        |     |     |    |
        |     |     |  22 cm
        |     |     |    |
  +-----+-----+-----+----+----+  -+
  |           |          X----Y   |
  +-----------+---------------+  -+
```
answer, method and trap →
G21-B44 marksSINGA 2021 Assessment — Primary 4 (SMC Practice Book)
A picture frame is made up of 4 identical rectangular pieces joined together as a pinwheel. The area of each rectangular piece is 69 cm² and its breadth is 3 cm. A square picture fits exactly in the centre of the frame. What is the area of the picture?
```
  +--+------------------+
  |  |                  |
  |  +---------------+  |
  |  |               |  |
  |  |    picture    |  |
  |  |               |  |
  |  +---------------+  |
  |                  |  |
  +------------------+--+
     |<- 3 cm ->|  (the frame's width)
```
answer, method and trap →

S23-A172 marksmediumSingapore Math Challenge 2023 — Primary 4 Contest Paper

A rectangular piece of paper was folded differently on both ends as shown below. What is the area of the rectangular piece of paper before it was folded? Give your answer in cm².

                                    |<- 4 cm ->|
                                    +----------+  -+ 1 cm
            +-----------------------+         /   -+
           /                        |        /
          /       9 cm              |       /
         +------------------------- +------+
         |                        
   3 cm  |
         +------------

  both creases are at 45 degrees

answer, method and trap →

S23-A182 marksmediumSingapore Math Challenge 2023 — Primary 4 Contest Paper
A rectangular piece of paper was cut into 3 smaller rectangles with dimensions 9 cm by 12 cm, 9 cm by 2 cm, and 9 cm by 5 cm. Find the length of the paper before it was cut. Give your answer in cm.
```
  +----------+---+------+
  |          |   |      |     the three pieces, side by side
  |  12 cm   |2cm| 5 cm |     every piece is 9 cm tall
  +----------+---+------+
  |<--------- ? -------->|
```
answer, method and trap →
S23-A222 marksmediumSingapore Math Challenge 2023 — Primary 4 Contest Paper
The figure below is made up of 7 identical rectangles. The perimeter of the whole figure is 340 cm. Find the breadth of 1 such rectangle. Give your answer in cm.
```
  +----------+----------+   -+
  |          |          |    | breadth
  +--+--+--+--+--+------+   -+
  |  |  |  |  |  |
  |  |  |  |  |  |  length
  |  |  |  |  |  |
  +--+--+--+--+--+

  top row: 2 rectangles lying down
  bottom row: 5 rectangles standing up
```
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S23-A292 markshardSingapore Math Challenge 2023 — Primary 4 Contest Paper
The figure is made up of 2 identical squares overlapping each other. The unshaded rectangle where they overlap has an area of 10 cm². The total area of the shaded parts is 142 cm². Find the length of the square. Give your answer in cm.
```
  +----------+
  |  shaded  |
  |      +---+------+
  |      |   |      |
  +------+---+      |
         | shaded   |
         +----------+

  the small middle box is the overlap (unshaded), 10 cm2
```
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S23-A302 markshardSingapore Math Challenge 2023 — Primary 4 Contest Paper

A carpet is laid on a rectangular floor measuring 20 m by 13 m, leaving a border of 3 m around it. Find the area of the floor that is not covered by the carpet. Give your answer in square metres.

  |<------------- 20 m ------------->|
  +----------------------------------+  -+
  |            3 m                   |   |
  |   +--------------------------+   |   |
  |3m |         Carpet           |   | 13 m
  |   +--------------------------+   |   |
  |                                  |   |
  +----------------------------------+  -+

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S23-A382 markshardSingapore Math Challenge 2023 — Primary 4 Contest Paper
The figure shows a rectangular garden 12 m by 16 m with a footpath (shaded) running along the top, down the left side, and part-way down the right side. The width of the footpath is 2 m. The area of the garden not covered by the footpath is 124 m². Find the length of AB, the part of the right-hand edge below the footpath. Give your answer in m.
```
  |<------- 12 m ------->|
  +######################+  -+
  #######################|   |
  ##+----------------+###|   |
  ##|                |###|   |
  ##|                |###|   | 16 m
  ##|                |###+ A |
  ##|                |   |   |
  ##|                |   |   |
  ##+----------------+---+ B -+

  # = the 2 m footpath
```
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S23-A42 markseasySingapore Math Challenge 2023 — Primary 4 Contest Paper

The figure below is made up of 2 squares of different sizes. AG is 8 cm and DE is 6 cm. What is the length of AD? Give your answer in cm.

  |<------------- ? ------------->|
  A               B
  +---------------+---C-------+ D
  |               |           |
  |               |           |
  | 8 cm          |           | 6 cm
  |               |           |
  |               |           |
  +---------------+-----------+
  G               F           E

answer, method and trap →

S24-A152 marksSMC 2024 — Primary 4 (Grade 4) Contest Paper
A piece of paper is cut straight down into Square A and Rectangle B. The area of A is twice the area of B. The breadth of Rectangle B is 14 cm. What is the area of Square A?
```
  +----------------+---------+
  |                |         |
  |       A        :    B    |     the cut is straight down,
  |    (square)    :         |     so A and B are the same height
  |                |         |
  +----------------+---------+
                   |<- 14 cm ->|
```
- (A) 28 cm²
- (B) 112 cm²
- (C) 336 cm²
- (D) 784 cm²
answer, method and trap →
S24-A62 marksSMC 2024 — Primary 4 (Grade 4) Contest Paper
The figure below is made up of 5 identical squares in an I-shape — two across the top, one in the middle, two across the bottom. The area of each square is 36 cm². What is the perimeter of the figure?
```
  +------+------+
  |      |      |
  +------+------+
         |      |
         |      |
  +------+------+
  |      |      |
  +------+------+

  5 identical squares, 36 cm2 each
```
- (A) 60 cm
- (B) 72 cm
- (C) 120 cm
- (D) 180 cm
answer, method and trap →

S24-B54 marksSMC 2024 — Primary 4 (Grade 4) Contest Paper

Square A and Rectangles B, C and D form the rectangle WXYZ. A sits top-left and is a square of side 7 cm, B is top-right, D is bottom-left and C is bottom-right. The area of Rectangle B is twice the area of Rectangle D. The shaded part (A, B and D together) has an area of 385 cm². Find the area of Rectangle C, in cm².

  W                                X
  +--------+-----------------------+
  |   A    |           B           |   7 cm
  |(square)|                        |
  +--------+-----------------------+
  |   D    |           C           |
  |        |                       |
  +--------+-----------------------+
  Z                                Y

  A is a 7 cm square · B = 2 x D · shaded (A + B + D) = 385 cm2

answer, method and trap →

S24-C35 marksSMC 2024 — Primary 4 (Grade 4) Contest Paper
Sam used Square X (side 5 cm), Rectangle Y (9 cm by 4 cm) and Rectangle Z (14 cm by 3 cm) — with a second copy of Square X — to form Figure A: Z lies along the bottom, one X sits on Z at the left, Y stands upright beside it, and the other X sits at the right-hand end, level with the bottom of Z. What is the perimeter of Figure A, in cm?
```
          +---+
          |   |
          | Y |               X = 5 by 5 (square)
    +-----+   |               Y = 9 tall, 4 wide
    |  X  |   |               Z = 14 wide, 3 tall
    |     |   |          +-----+
    +-----+---+----------+  X  |
    |         Z          |     |
    +--------------------+-----+

              Figure A

  note the STEP on the right: the square stands 2 cm proud of Z
```
answer, method and trap →
S24-C55 marksSMC 2024 — Primary 4 (Grade 4) Contest Paper
A rectangular park measures 54 m by 28 m. A pedestrian path 2 m wide and a cyclist path 3 m wide are built along two sides of the park — the pedestrian path wraps the top and left of the park, and the cyclist path wraps the top and left of that. It costs $18 to construct each square metre of the cyclist path. How much does it cost to construct the cyclist path?
```
  ################################   -+ 3 m  cyclist
  ##+--------------------------+##   -+ 2 m  pedestrian
  ##|                          | #
  ##|          Park            | #    28 m
  ##|                          | #
  ##+--------------------------+-+
     |<-------- 54 m -------->|

  # = the two paths, along the TOP and the LEFT only
```
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M26-A62 marksSMC 2026 Mock Exam — Grade 4 (Geniebook)

The figure below is made up of 4 identical rectangles. Find the perimeter of the figure.

 |<----- 10 cm ----->|
                     +---+
                     |   |
                     |   |
                     |   |
 +-------------------+   |
 +---------------+---+---+---------------+  -+- 2 cm
                 |   +-------------------+  -+-
                 |   |
                 |   |
                 |   |
                 +---+

 4 identical rectangles, each 10 cm long and 2 cm wide, set as a
 pinwheel: turn the figure a quarter turn and it looks the same.

(1) 96 cm
(2) 80 cm
(3) 40 cm
(4) 36 cm

answer, method and trap →

M26-B24 marksSMC 2026 Mock Exam — Grade 4 (Geniebook)

The figure is made up of 2 identical squares and 3 identical rectangles. What is the length of the unknown side?

                         +-----------+  -+
                         |           |   |
                         |  square   |   |
                         |           |   |
  |<-------- ? --------->|           |   |
  +-----------+----------+-----------+   |
  |           |      rectangle       | 18 cm
  |           +----------------------+   |
  |  square   |      rectangle       |   |
  |           +----------------------+   |
  |           |      rectangle       |   |
  +-----------+----------------------+  -+
  |<------------ 26 cm ------------->|

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M26-B54 marksSMC 2026 Mock Exam — Grade 4 (Geniebook)
Barry has a garden with an area of 216 m². It is made up of a rectangle and a square. The area of the rectangle is 5 times the area of the square. Barry wants to build a fence around part of his garden as indicated by the dashes in the figure. Given that the breadth of the rectangle is 9 m, how many metres of fence does he need?
```
  - - - - - - - - - - - - - - - -   -+
  '                              '    |  9 m
  '          rectangle           '    |
  - - - - - - - -+------+- - - - -   -+
                 '      '
                 ' squ. '
                 '      '
                 +- - - +

  the dashed line is the fence (the whole outline)
```
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M26-B94 marksSMC 2026 Mock Exam — Grade 4 (Geniebook)

The figure below shows Marcus's backyard with 2 identical 8-m square ponds. What is the remaining area of the empty space around the two ponds in the backyard?

  |<-------------- 20 m -------------->|
  +------------------------------------+  -+
  |                                    |   |
  |   +----------+    +----------+     |   |
  |   |  pond    |    |  pond    |     |   |
  |   |  8 m sq  |    |  8 m sq  |     | 15 m
  |   +----------+    +----------+     |   |
  |                                    |   |
  +------------------------------------+  -+

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M26-C15 marksSMC 2026 Mock Exam — Grade 4 (Geniebook)

After a rectangular piece of paper was cut into a maximum of 18 squares of sides 4 cm each, an L-shaped strip of paper was left over as shown. Given that the length of the rectangular piece of paper is 26 cm, what is the perimeter of the rectangular piece of paper before it was cut?

  +--+------------------------------+
  |  |                              |
  |  |                              |
  |  |    the 18 squares of 4 cm    |
  |  |                              |
  |  |                              |
  +--+------------------------------+
  |              strip              | -+- 1 cm
  +---------------------------------+ -+-
  |<------------ 26 cm ------------>|

  the leftover L-strip is the narrow band down the left edge
  plus the 1 cm band along the bottom

answer, method and trap →

M26-C35 marksSMC 2026 Mock Exam — Grade 4 (Geniebook)
The figure is not drawn to scale. It is made up of two identical rectangles overlapping each other, forming Square A. The area of Square A is 9 cm² and the area of each rectangle is 50 cm². The length of the rectangle is twice its breadth. Find the perimeter of the figure.
```
                  +---------+
                  |         |
                  |         |
                  |         |
     +------------+---+     |
     |            | A |     |
     |            +---+-----+
     |                |
     +----------------+

  Square A is where the two rectangles overlap
```
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ELFA-46 Generated by make topics. 26 questions from the bank, filed under geometry.area-perimeter in the geometry family.