Question

Find the area of quadrilateral ABCD.

Answer 1

Hint: In order to compute the area of the given quadrilateral, we apply the formula for the area of quadrilateral using the data given in the question. First we find the diagonal lengths of the quadrilateral.

Complete step-by-step answer:
We know the formula for Area of quadrilateral ABCD =$\dfrac{1}{2}{\text{d}}\left( {{{\text{h}}_1} + {{\text{h}}_2}} \right)$
From the figure, Sum of the length of perpendicular from the remaining two vertices on the diagonal AC = (${{\text{h}}_1} + {{\text{h}}_2}$).
⟹${{\text{h}}_1} + {{\text{h}}_2}$ = 12cm.
Length of the diagonal BD = 11cm.
∴Area of the quadrilateral ABCD = $\dfrac{1}{2}{\text{d}}\left( {{{\text{h}}_1} + {{\text{h}}_2}} \right)$= $\dfrac{1}{2} \times 12 \times 11$= $6 \times 11$= 66${\text{c}}{{\text{m}}^2}$.

Note: In order to solve questions of this type the key is to have adequate knowledge in formulae for areas of quadrilaterals. Then according to the figure we observe the lengths and diagonals of the quadrilateral to compute its area. The area of a quadrilateral is expressed in square units.