Question

Two parallel sides of trapezium are 120 and 154 and otehr two are 50 and 52 find area

Answer 1

ANSWER:-

Given:

Two parallel sides of trapezium are 120cm and 154cm & other two are 50cm & 52cm.

To find:

Find the area.

Solution:

Draw a line DE parallel to AB & draw a Perpendicular DF on CB.

It can be observed that ABED is a parallelogram.

BE= AD= 120cm

ED= AB= 50cm

EC= 154 - BE = 154-120 = 34cm.

Now,

Using the Heron's Formula, we get;

For ∆DEC,

Semi-perimeter,

$= > \frac{a + b + c}{2}$

$= > \frac{50 + 52 + 34}{2} \\ \\ = > \frac{136}{2} \\ \\ = > 68cm$

Therefore,

Area of ∆,

$= > \sqrt{s(s - a)(s - b)(s - c)}$

Area of ∆DEC,

$= > \sqrt{68(68 - 50)(68 - 52)(68 - 34)} \\ \\ = > \sqrt{68(18)(16)(34)} \\ \\ = > \sqrt{68 \times 18 \times 16 \times 34} \\ \\ = > \sqrt{665856} \\ \\ = > 816 {cm}^{2}$

Area of ∆ DEC;

$= > \frac{1}{2} \times EC\times DF \\ \\ = > 816 = \frac{1}{2} \times 34 \times DF \\ \\ = > DF = \frac{1632}{34} \\ \\ = > DF= 48cm$

Now,

Area of trapezium:

$= > \frac{1}{2} \times (AD + BC) \times DF \\ \\ = > \frac{1}{2} \times (120 + 154) \times 48 \\ \\ = > \frac{1}{2} \times 274 \times 48 \\ \\ = > 274 \times 24 \\ \\ = > 6576cm {}^{2}$

Hope it helps ☺️