Question

b) The area of a trapezium with equal non-parallel sides is 168 m2. If the lengths of the
parallel sides are 36 m and 20 m as shown in Fig. 1, find the length of the non-parallel
sides.​

Answer 1

$\sf{\huge{\underline{\orange{Given :-}}}}$

• The area of a trapezium with equal non-parallel sides is 168 m².

• The lengths of the parallel sides are 36 m and 20 m .

$\sf{\huge{\underline{\blue{To\:Find :-}}}}$

• The length of the non-parallel sides.

$\sf{\huge{\underline{\purple{Solution :-}}}}$

Given, The area of a trapezium with equal non-parallel sides is 168 m².

We know, The area of a trapezium = ½ × sum of || sides × hieght

➝ 168 = ½ ×( 36 + 20) × hieght

➝ 168 = ½ × 56 × hieght

➝ 168 = 28 × hieght

➝ hieght = 168 / 28

➝ hieght = 6 m

From fig.in attachment,

Take ΔABC , use P.G.T.

(AB)² = (BC)² + (AB)²

➝ (AB)² = (8)² + (6)²

➝ (AB)² = 64 + 36

➝ (AB)² = 100

➝ (AB) = √ 100

➝ AB = 10m

Hence, The length of the non-parallel sides 10 m.