Question

6. The diagonal of a quadrilateral shaped field is 24m and the remaining opposite verticals are 8m and 13 m. Find the area of the field.?? ​

Answer 1

Answer :-

• The area of quadrilateral is 372m².

Step-by-step explanation:

To Find :-

• The area of quadrilateral.

Solution:

Given that,

• The diagonal of quadrilateral shaped field = 24m
• The opposite verticals are 8m and 13m

As we know that,

$\bigstar \: \: \boxed{\bf{Area \: of \: quadrilateral = \dfrac{1}{2} \times diagonal \times ({h}_{1} + {h}_{2})}}$

Where,

• $\sf{{h}_{1}}$ and $\sf{{h}_{2}}$ are two heights of two triangles.

Therefore,

$\bf{ \longmapsto \: \dfrac{1}{2} \times diagonal \times ({h}_{1} + {h}_{2})} \\ \\ \\ \\ \bf{ \longmapsto \: \dfrac{1}{2} \times 24 \times (18 + 13)} \\ \\ \\ \\ \\ \bf{ \longmapsto \: \dfrac{1}{2} \times 24 \times 31} \\ \\ \\ \\ \bf{ \longmapsto \: \dfrac{1}{ \cancel{2}} \times \cancel{24} \times 31} \\ \\ \\ \\ \bf{ \longmapsto \: 1 \times 12 \times 31} \\ \\ \\ \\ \bf{ \longmapsto \: 12 \times 31} \\ \\ \\ \\ \bf{ \longmapsto \: \red{372}}$

Hence, The area of quadrilateral is 372m².