Question

1. The diagonals of a quadrilateral is 30cm in length and the lengths of perpendiculars to it from the opposite vertices are 8cm and 10cm. Find the area of the quadrilateral ?


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Answer 1

Answer:

The area of the quadrilateral is $270\;cm^{2}.$

Step-by-step explanation:

Given: The diagonals of a quadrilateral is $30$ cm in length and the lengths of perpendiculars to it from the opposite vertices are $8$ cm and $10$ cm.

To Find: The area of the quadrilateral.

Solution: From the below figure it is clear that,

Diagonal $= 30$ cm,

$AB = 8$ cm,

$BC = 10$ cm.

Now, to find the area of the quadrilateral use the formula,

$Area\;of\;the\;quadrilateral = \frac{1}{2} \times diagonal \times (Sum\; of \; two \; sides)$

                                         $=\frac{1}{2} \times30\times(AB+BC)\\=15\times(8+10)\\=15\times18\\=270 \; cm^{2}$

Hence, the area of the quadrilateral is $270\;cm^{2}.$