Question

The diagonal of a quadrilateral shaped field is 26 m and the perpendiculars dropped on it from the remaining opposite vertices are 12 m and 5 m. Find the area of the field.

212 m²

442 m²

221 m²

440 m²

Answer 1

Answer:

221 m²

Step-by-step explanation:

REFER TO IMAGES FOR EXPLANATION

hope it helps you

Answer 2

$\large{\underbrace{\sf{\purple{Required\:Answer:}}}}$

$\Huge{\boxed{\sf{\red{ 221m^{2}}}}}$

$\large{\underbrace{\sf{\pink{Explanation:}}}}$

:$\implies{\large{\boxed{\sf{\orange{Area\:of\:the\:quadrilateral= \dfrac{1}{2} \times Diagonal \times (Sum\:of\:perpendicular\:lines)}}}}}$

:$\implies{\sf{ \dfrac{1}{2} \times 26m \times (12m+5m)}}$

:$\implies{\sf{ 13m \times 17m}}$

:$\implies{\sf{ 13m \times 17m}}$

:$\large\implies{\boxed{\sf{\red{ 221m^{2}}}}}$

$\large{\underbrace{\sf{\green{Alternate\:Method:}}}}$

We can also find the area by calculating the area of triangles and then add them.

:$\implies{\large{\boxed{\sf{\orange{Area\:of\:the\:triangle= \dfrac{1}{2} \times (Base) \times (Height)}}}}}$

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