Question

in a Trapezium the measure of parallel sides are 10 centimetre and 20 centimetre its non parallel side are congruent each measuring 13 cm find the area of the trapezium​

Answer 1

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ABCD be the given trapezium in which AB = 20 cm, DC = AE= 10 cm, BC = 13 cm and AD = 13cm.

Through C, draw CE || AD, meeting AB at E.

Draw CF ⊥ AB.

Now, EB = (AB - AE) = (AB - DC)

EB = (20- 10) cm = 10 cm;

CE = AD = 13 cm; AE = DC = 13 cm.

Now, in ∆EBC, we have CE = BC = 13 cm.

It is an isosceles triangle.

Also, CF ⊥ AB

So, F is the midpoint of EB.

Therefore, EF = ¹/₂ × EB = 1/2× 10= 5cm.

Thus, in right-angled ∆CFE, we have CE = 13 cm, EF = 5 cm.

By Pythagoras’ theorem, we have

CF = [√CE² - EF²]

CF = √(13² - 5²)

CF= √169-25= √144 = √12×12

CF= 12cm

Thus, the distance between the parallel sides is 12 cm.

Area of trapezium ABCD = ¹/₂ × (sum of parallel sides) × (distance between them)

Area of trapezium ABCD = ¹/₂ × (20 + 10) × 12 cm²

Area of trapezium ABCD = 1/2×(30)× 12

Area of trapezium ABCD= 30×6 = 180 cm²

Hence, Area of trapezium ABCD= 180 cm²
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