Question

The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm,

find the area of the trapezium.​

Answer 1

The distance between both non parallel sides is called height
Area of trapezium is
1/2*sum of parallel sides *height
1/2 *40 +20 *24
1/2*60*24
30*24
=720

Answer 2

Given:

The parallel sides of trapezium = 40cm and 20cm.

The non-parallel sides of trapezium = 26cm = 26cm.

To Find:

The area of the trapezium.

Solution:

Assume a trapezium ABCD.

where, ABIICD, AD = BC, AB = 20cm, BC = 26cm, CD = 40cm, and DA = 26cm.

Now, Let AE and BF be the perpendiculars drawn on DC.

Consider triangle DAE, ∠A =90°,

By Pythagoras theorem,

H² = P² + B².

Here, H = AD = 26cm and B = DE = 10cm.

so, P² = 26² - 10².

P² = 676 - 100.

P² = 576cm².

P = AE = 24cm.

Now, By the area of the trapezium,

Area of trapezium = 1/2 × sum of parallel sides × distance between the parallel sides.

Area of trapezium ABCD = 1/2 × (AB + CD) × AE.

Area of trapezium ABCD = 1/2 × (20+40) × 24.

Area of trapezium ABCD = 1/2 × 60 × 24.

Area of trapezium ABCD = 720cm².

Hence, The area of trapezium ABCD is 720cm².