Question

In a trapezium ABCD, AB || DC, AB = 30 cm, BC
= 15 cm, DC = 44 cm and AD = 13 cm. Find the
area of the trapezium.
Please give step by step clear explanation

Answer 1

Question:-

• In a trapezium ABCD, AB || DC, AB = 30 cm, BC = 15 cm, DC = 44 cm and AD = 13 cm. Find the area of the trapezium.

Given:-

• ABCD is a trapezium
• AB||DC
• AB=30cm
• BC=15 cm
• DC=44 cm
• AD=13 cm

To find:-

• The area if trapezium

Solution:-

$\purple \dag \: \boxed{ \underline{ \red{ \mathbf{Semi-perimeter = \frac{30 + 44 + 13 + 15}{2} = 51}}}}$

$\boxed{ \pink{ \sf{area \: of \: trapezium = \sqrt{(s - a)(s - b)(s - a - c)(s - a - d)}. \frac{(a + b)}{(b - a)} }}}$

$= \frac{30}{44} - \sqrt{(51 - 30).7(51 - 30 - 13).(51 - 30 - 15)}$

$= \frac{74}{14} . \sqrt{21.7.8.6}$

$= \frac{37}{7} .7 \sqrt{3.3.2.8}$

$= 37 \times 3 \times 4 = 37 \times 12$

$= 444 {cm}^{2}$

Therefore the area of trapezium is 444cm².