Question

The diagonal of a quadrilateral shaped field is 36 m and the perpendicualr dropped on it from the remaining opposite vertices  are 9 m (h1) and 13 m (h2). Find the area of the field. 

396 m²
792 m²
175 m²
117 m²​

Answer 1

$\\ \color{violet} \large\underline{\sf \: Question :- }$

The diagonal of a quadrilateral shaped field is 36 m and the perpendicualr dropped on it from the remaining opposite vertices  are 9 m (h1) and 13 m (h2). Find the area of the field. 

$\\ \color{violet} \large\underline{\sf \: Solution :- }$

$\\ \\ \sf \: \: \: \: Given$

$\\ \\ \sf \: \: Length \: of \: diagonal = d = 36 \: m$

$\\ \\ \sf \: \: Length \: of \: perpendicular \: dropped \: on \: BD \\ \sf h_1= 13 \: m \: and \: h_2 = 9 \: m$

$\\ \\ \sf \: \: Now,$

$\\ \\ \sf \: \: Area \: of \: ABCD \: = \: \frac{d}{2} \times (h_1 + h_2)$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: \frac{36}{2} \times (13 + 9)$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: \frac{36}{2} \times 22$

$\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: 18 \times 22$

$\\ \\ \: \therefore \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{\boxed{ \orange{\tt Area \: of \: ABCD \: = \: 396 {m}^{2} }}}$

So, Option A is correct.

Answer 2

$\underline{\boxed{\bold{ \bigstar \; Question \; \bigstar }}}$ $\; \; \; \;$

The diagonal of a quadrilateral shaped field is 36 m and the perpendicular dropped on it from the remaining opposite vertices  are 9 m $(h_{1} )$ and 13 m $(h_{2} )$. Find the area of the field.  

a) 396 m²

b) 792 m²

c) 175 m²

d) 117 m²​

$\underline{\boxed{\bold{ \bigstar \; Answer \; \bigstar }}}$ $\; \; \; \;$

Given:-

Length of diagonal = 36cm

Length of perpendicular dropped on AC/BD -

h_{1} = 9m

h_{2} = 13m

Let the length of diagonal be 'd'

So, area of ABCD = $\frac{d}{2}$ × ($h_{1}$ + $h_{2}$)

                       = $\frac{36}{2}$ × (9 + 13)

                       = 18 × 22

                        = 396m²

∴ Area of field ABCD = 396m²

⇒ Option A is correct.

Hope this helps uh! ♡