Question

A diagonal of a quadrilateral is 24 cm in length and the lengths of the perpendiculars to it from the opposite vertices are 5 cm and 8 cm.Find the area of the quadrilateral.​

Answer 1

Answer:

area of quadrilateral= 1/2*D*(H1+H2)

=1/2*24*13

12*13=  156

hope it helps

pls mark as brainliest

Answer 2

Answer:

Let ABCD be the Quadrilateral with diagonal AC such that

AC = 24cm. Let BL and DM be the perpendiculars drawn from the vertices B and D respectively to diagonal AC.

Then, BL = 5cm and DM = 8cm.

Area of Quadrilateral ABCD = Area (∆ABC)+ Area (∆ADC)

$= \frac{1}{2} \times AC \times BL + \frac{1}{2} \times AC \times DM$

$area \: of \: a \: triangle \: = \\ \frac{1}{2} \times base \times height \: and \\ \: taking \: AC \: as \:base \: of \: ∆ABC and ∆ADC$

$\frac{1}{2} \times AC(BL + DM) \\ \\ \frac{1}{2} \times 24cm \: \times (5cm \: + 8cm) \\ \\ = 12cm \: \times (13cm) \: = {156cm}^{2}$

✅ hence the area of the Quadrilateral is 156cm².

Hope it helps you ⛄