Question

The diagonal of a quadrilateral shaped field is 20 m and the perpendicular dropped on
it from the remaining opposite vertices are 15 m and 5 m. Find the area of the field.

Answer 1

Answer:

Given :-

The diagonal of a quadrilateral shaped field is 20 m and the perpendicular dropped on it from the remaining opposite vertices are 15 m and 5 m.

To Find :-

What is the area of the field.

Formula Used :-

$\clubsuit$ Area Of Quadrilateral :

$\longmapsto \sf\boxed{\bold{\pink{A =\: \dfrac{1}{2}d(h_1 + h_2)}}}$

where,

A = Area

d = Diagonal

h₁ and h₂ = Height

Solution :-

Given :

Diagonal (d) = 20 m

Height (h₁) = 15 m

Height (h₂) = 5 m

According to the question by using the formula we get,

$\implies \sf Area\: of\: field =\: \dfrac{1}{2} \times 20 \times (15 + 5)$

$\implies \sf Area\: of\: field =\: \dfrac{\cancel{20}}{\cancel{2}} \times (20)$

$\implies \sf Area\: of\: field =\: \dfrac{10}{1} \times (20)$

$\implies \sf Area \: of\: field =\: 10 \times 20$

$\implies \sf\bold{\red{Area\: of\: field =\: 200\: {m}^{2}}}$

$\therefore$ The area of field is 200 m².