# PSLE 2023 Circle and Trapezium Math Questions In this revision note, we will go through PSLE 2023 Circle and Trapezium questions so that your child will become better at solving area and perimeter questions.

These questions assess your child’s agility in visualizing and fitting various shapes.

Before you read on, you might want to download this entire revision notes in PDF format to print it out for your child, or to read it later.

This will be delivered to your email inbox. ## PSLE 2023 Math Circle Question Each circle has a radius of 7 cm.

a) Find the perimeter of the shaded part.

b) Find the area of the shaded part.

Take π as 22/7.

Solutions

a) Perimeter = the total lengths outside the shaded part Let’s break up the perimeter into 3 parts. Observe that each part is the circumference of a circle.

3/4 Circle + 1/4 Circle

= 1 circle

Diameter of circle = 7 x 2 = 14 cm

The perimeter of the shaded part

= Circumference of 3 circles

= π × d × 3

= 22/7 × 14 × 3

= 132 cm (Ans)

b) To find the area, we can use the cut-and-paste method: = the rectangle + ½ circle + ½ circle

= 1 rectangle + 1 circle

Length of rectangle = 7 cm x 4

= 28 cm

Breadth of rectangle = 7 cm x 2

= 14 cm

Area of rectangle = 28 cm x 14 cm

= 392 cm2

Area of circle = 22/7 x 7 x 7

= 154 cm2

Shaded area = 392 cm2 + 154 cm2

= 546 cm2  (Ans)

## PSLE 2023 Math Trapezium Question

The figure shows a trapezium with a perimeter of 96 cm. a) Figure A is made up of 3 such trapeziums and has a perimeter of 204 cm. Find the length of PQ.

b) Figure B is made up of 4 such trapeziums and has an area of 1932 cm2. Given that CD = 12 cm, find the length of PS. Solutions

a) Breaking Figure A into the 3 trapeziums, we see that 4 PQs (highlighted in yellow) are not counted in the perimeter of Figure A. Hence,

Perimeter of Figure A = Perimeter of 3 Trapeziums – 4 PQ

Perimeter of 3 Trapeziums = 3 x 96 cm = 288 cm

Perimeter of Figure A = Perimeter of 3 Trapeziums – 4 PQ

204 cm = 288 cm – 4 PQ

4 PQ = 288 cm – 204 cm = 84 cm

PQ = 84 cm ÷ 4 = 21 cm (Ans)

b) Observe that 2 trapeziums can form a rectangle in Figure B. Area of 4 trapeziums = 1932 cm2

Area of 2 trapeziums = 1932 cm2 ÷ 2

= 966 cm2

Area of rectangle = 966 cm2

Breadth of rectangle = PQ = 21 cm (from part a)

Length of rectangle = Area of rectangle ÷ Breadth

= 966 cm2 ÷ 21 cm

= 46 cm PS is the shorter parallel side of the trapezium.

PS = 46 – 12 – 21 = 13 cm (Ans)

Test your child’s understanding by taking this short quiz!

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Before you go, you might want to download this entire revision notes in PDF format to print it out for your child, or to read it later.

This will be delivered to your email inbox.  Ms Nelly Ke
Math Specialist
Jimmy Maths and Grade Solution Learning Centre

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