Question

A quadrilateral has one of its diagonal 14.8cm the altitudes draw to this diagonal 8.4cm and 5.7 cm find its area

Answer 1

Given:

One of the diagonal of the quadrilateral = 14.8 cm

Altitudes drawn to this diagonal are 8.4 cm and 5.7 cm.

To find:

The area of the quadrilateral

Solution:

We know that

The area of a quadrilateral is half the product of the length of one of its diagonal "d" and the sum of the length of altitudes "h₁" & "h₂" drawn from opposite vertices to that diagonal.

$\boxed{\boxed{\bold{Area = \frac{1}{2} \times d\times [h_1+ h_2] }}}$

Here

d = 14.8 cm

h₁ = 8.4 cm

h₂ = 5.7 cm

Therefore, substituting the values in the formula, we get

Area of the given quadrilateral is,

= $\frac{1}{2} \times 14.8 \times [8.4\: + \:5.7]$

= $\frac{1}{2} \times 14.8 \times 14.1$

= $7.4 \times 14.1$

= $\bold{104.34\:cm^2}$

Thus, its area is 104.34 cm².

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