Class 8 Area of Polygons — practice questions with answers

Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. What is the area of a trapezium with parallel sides 10 cm and 6 cm and height 4 cm?

A32 sq cm
B40 sq cm
C64 sq cm
D16 sq cm

Show answer

Answer: A) 32 sq cm

Area =

\frac{1}{2}

(a+b)h =

\frac{1}{2}

(10+6)(4) =

\frac{1}{2}

(16)(4) = 32 sq cm.

2. The area of a rhombus is 150 sq cm and one diagonal is 20 cm. Find the length of the other diagonal.

A15 cm
B30 cm
C7.5 cm
D10 cm

Show answer

Answer: A) 15 cm

150 =

\frac{1}{2}

(20) d = 10 d, so d = 15 cm.

3. A rhombus has side 13 cm and one diagonal 24 cm. Find its area. (Use the fact that diagonals bisect at right angles.)

A120 sq cm
B156 sq cm
C240 sq cm
D60 sq cm

Show answer

Answer: A) 120 sq cm

Half-diagonal = 12. Other half =

1 3^{2} - 1 2^{2}

169 - 144

25

= 5, so other diagonal = 10. Area =

\frac{1}{2}

(24)(10) = 120 sq cm.

4. A trapezium-shaped plot has parallel sides 35 m and 25 m and height 24 m. It is to be fenced and levelled. Levelling costs Rs 8 per square metre.
Find the cost of levelling.

ARs 5760
BRs 2880
CRs 11520
DRs 720

Show answer

Answer: A) Rs 5760

Area =

\frac{1}{2}

(35+25)(24) =

\frac{1}{2}

(60)(24) = 720 sq m. Cost = 720 x 8 = Rs 5760.

5. A trapezium has parallel sides 26 cm and 14 cm and the two non-parallel (slant) sides are each 10 cm.
Find the area of the trapezium. (Hint: drop perpendiculars from the top corners.)

A160 sq cm
B200 sq cm
C120 sq cm
D240 sq cm

Show answer

Answer: A) 160 sq cm

The base overhang on each side =

\frac{26 - 14}{2}

= 6 cm. Height =

1 0^{2} - 6^{2}

100 - 36

64

= 8 cm. Area =

\frac{1}{2}

(26+14)(8) =

\frac{1}{2}

(40)(8) = 160 sq cm.

Practise all 50 questions free →

10 free questions a day without an account — unlimited with a free account.