Question

Find area of quadrilateral whose diagonal is 24m and perpendiculars on it are 10m and 12m.​

Answer 1

Given :

• Diagonal of quadrilateral = 24m
• Length of perpendiculars = 10m and 12m

To Find :

• Area of quadrilateral

Formula Using :

$\Large\begin{gathered} {\underline{\boxed{ \rm {\red{Area \: = \: \frac{1}{2} \: \times \: d \: \times \: ( h_1 + h_2) }}}}}\end{gathered}$

• d denotes diagonal
• h1 and h2 denotes length of perpendiculars

Solution :

$\tt \large \green\leadsto \:Area \: = \: \frac{1}{2} \: \times \: d \: \times \: ( h_1 + h_2) \: \: \: \\ \\ \tt \large \green\leadsto \:Area \: = \: \frac{1}{2} \: \times \: 24 \: \times \: ( 10 + 12) \\ \\ \tt \large \green\leadsto \:Area \: = \: \frac{1}{2} \: \times \: 24 \: \times \: ( 22) \: \: \: \: \: \: \: \: \: \\ \\ \tt \large \green\leadsto \:Area \: = \: \frac{1}{ \cancel2} \: \times \: \cancel{24}\: ^{\rm \ \purple{12} } \: \times \: ( 22) \: \: \: \\ \\ \tt \large \green\leadsto \:Area \: = \: 12 \: \times \: 22 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \tt \large \green\leadsto \:Area \: = \: 264 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence , the area of quadrilateral is 264 cm²