In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is ____

c
m
2

.

Question

In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is ____

c
    m
    2

.

Infinity Learn · Accepted Answer

In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is 40

c m 2

.
Given ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm.
In the adjoining figure,ABCD is a trapezium in which AB||DC;AB=7 cm;AD=BC=5 cm and the distance between AB and DC is 4 cm.Find the length of DC and hence,find the area of trap,ABCD.

In the adjoining figure,ABCD is a trapezium in which AB||DC;AB=7 cm;AD=BC=5 cm and the distance between AB and DC is 4 cm.Find the length of DC and hence,find the area of trap,ABCD.

Applying Pythagoras theorem in triangle ADL,

h y p o t e n o u s 2 = b a s e 2 + p e r p e n d i c u l a r 2

A D 2 = A L 2 + D L 2 52 = 42 + D L 2 D L 2 = 52 − 42 D L = 25 − 16 D L = 9 D L = 3 cm

Applying Pythagoras theorem in triangle BCM,

h y p o t e n o u s 2 = b a s e 2 + p e r p e n d i c u l a r 2

B C 2 = B M 2 + M C 2 52 = 42 + M C 2 M C 2 = 52 − 42 M C = 25 − 16 M C = 9 M C = 3 cm

Now length DC is,

D C = D L + L M + M C D C = 3 + 7 + 3 D C = 13 cm

Area of trapezium is,

A = h (a + b) 2 A = 12 × (A B + D C) × A L A = 12 × (7 + 13) × 4 A = 40 cm 2

Area of trapezium is 40

c m 2

.

In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is ____ $c m 2$ .

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In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is ____ c m 2 .

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Detailed Solution

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In the adjoining figure, ABCD is a trapezium in which AB || DC, AB = 7 cm, AD = BC = 5 cm and the distance between AB and DC is 4 cm. The area of trapezium ABCD is ____ $c m 2$ .