Question

The parallel sides of a trapezium are 15m and 10m long and its non parallel sides are 8m and 7m long. Find the area of the trapezium

Answer 1

Solution:

Length of Parallel sides of trapezium = 15 m and 10 m

Length of non parallel sides = 8 m and 7 m

As , you must keep in mind

Area of Trapezium = $\frac{1}{2}\times [\text{Sum of parallel Sides} ] \times [\text{Perpendicular Distance between them}]$

Draw ,CM ⊥AB and D N⊥AB

CD ║AB, and  ∠DNM + ∠CMN= 180°

So, Quadrilateral DNMC is a rectangle.

MN= 10 m, AN = (5-x ) m, MB= x cm, DN = MC= h m

In Δ DNA

AD²=AN²+ND² →→[By Pythagoras theorem]

8²= (5-x)² + h²

1.→ h²= 8²- (5-x)²

In Δ BMC

7² = h² + x²

2.→ h²= 7²- x²

Equating 1 and 2

8²- (5-x)²=7²- x²

⇒64-49-25+10 x-x²= -x²

⇒ 1 0 x = 10

Dividing both sides by 10

x=1

h²= 7²-1²

h²= 48

h=4 √3 m

Area of trapezium = $\frac{1}{2} \times 4 \sqrt{3} \times (15+ 10) \\\\ \frac{173.2}{2} \\\\ = 86.60$ meter square

Use ,√3=1.732

Answer 2

$\sqrt[2]{3}$

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