Question

Two parallel sides of a trapezium are 58 cm and 42 cm. The other two sides are of
equal lengthwhich is 17 cm. Find the area of trapezium,​

Answer 1

Answer:850cm²

Step-by-step explanation:

Answer 2

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Given

• Parallel sides of trapezium is 58cm and 42cm.
• Non - parallel sides of trapezium is 17cm each

To Calculate

• Area of Trapezium

Constitution

• Through C, draw CF || AD
• CE ⊥ AB

Solution

Now, PC = DC - DP = 58 - 42 = 16cm

In △PBC, PB = PC = 15cm

So, it is an isosceles triangle.

Also, BQ ⊥ PC. So, Q is the mid point of PC.

PQ = 1/2 PC = 1/2 × 16 = 8cm

In a right angle triangle BQP,

$\bf {bp}^{2} = {pq}^{2} + {bq}^{2} (by \: pythagoras \: theorem)$

$\bf \implies {17}^{2} = {8}^{2} + {bq}^{2}$

$\bf \implies 289 = 64 + {bq}^{2}$

$\bf \implies 289 - 64 = {bq}^{2}$

$\bf \implies 225 = {bq}^{2}$

$\bf \implies {bq}^{2} = 225$

$\bf \implies bq = \sqrt{225}$

$\bf \implies bq = 15cm$

Area of Trapezium ABCD

$\bf = \frac{1}{2} (AB + DC) × BQ$

$\bf = \frac{1}{2} (42 + 58) \times 15$

$\bf = \frac{1}{2} \times 100\times 15$

$\bf = 50 \times 15$

$\bf = {750cm}^{2}$

Therefore, Area of Trapezium is 750cm².