# 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.

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## 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.*

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__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**:

Shaded area

= 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 cm^{2}

Area of circle = 22/7 x 7 x 7

= 154 cm^{2}

Shaded area = 392 cm^{2} + 154 cm^{2}

= 546 cm^{2 }(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 cm^{2}. 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 cm^{2}

Area of 2 trapeziums = 1932 cm^{2} ÷ 2

= 966 cm^{2}

Area of rectangle = 966 cm^{2}

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

Length of rectangle = Area of rectangle ÷ Breadth

= 966 cm^{2} ÷ 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.**

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To Your Child’s Success,

Ms Nelly Ke

Math Specialist

Jimmy Maths and Grade Solution Learning Centre

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