Question

the diagonals of a quadrilateral shaped field is 24m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 30m. find the area of the field ​

Answer 1

Answer:

456 m.sq.

Step-by-step explanation:

Let ABCD is Quadrilateral and AC is diag of 24 m.

From AC We have 2 Prependiculars in opposite sides.

8 and 30 m

Using area Of triangle ew find area of whole field.

In tri(ABC) ar=1/2*24*8=96 m sq

In tri(ADC) ar=1/2*24*30=360 m sq

Add Ar Of both triangles we get field area

=456 m sq

Answer 2

Step-by-step explanation:

$\tiny \bigstar \: \: \underline{ \boxed{\sf Area \: of \: Quadrilateral = \dfrac{1}{2} \times Sum \: of \: the \: perpendiculars \: on \: the \: diagonal \: from \: opposite \: vertices}} \: \: \bigstar$

$: \implies\sf Area \: of \: Quadrilateral = \dfrac{1}{2} \times 24 \times (8 + 13)$

$: \implies\sf Area \: of \: Quadrilateral = \dfrac{1}{ \cancel{2}} \times \cancel{24} \times 21$

$: \implies\sf Area \: of \: Quadrilateral = 12 \times 24$

$: \implies \underline{ \boxed{\sf Area \: of \: Quadrilateral = 252 \: {m}^{2} }} \\ </p><p>$