Question
In Figure, ABCD is a quadrilateral in which diagonal AC = 84cm; $\text{DL}\bot\text{AC},\text{BM}\bot\text{AC},$ DL = 16.5cm and BM = 12cm. Find the area of quadrilateral ABCD.
✓
Answer
We have,
AC = 84cm, DL = 16.5cm and BM = 12cm
Area of triangle ADC $=\frac{1}{2}(\text{AC}\times\text{DL})$
$=\frac{1}{2}(84\text{cm}\times16.5\text{cm})=693\text{cm}^2$
Area of triangle ABC $=\frac{1}{2}(\text{AC}\times\text{BM})$
$=\frac{1}{2}(84\text{cm}\times12\text{cm})=504\text{cm}^2$
Hence, Area of quadrilateral ABCD = Area of ADC + Area of ABC
$=(693+504) cm ^2=1197 cm^2$
AC = 84cm, DL = 16.5cm and BM = 12cm
Area of triangle ADC $=\frac{1}{2}(\text{AC}\times\text{DL})$
$=\frac{1}{2}(84\text{cm}\times16.5\text{cm})=693\text{cm}^2$
Area of triangle ABC $=\frac{1}{2}(\text{AC}\times\text{BM})$
$=\frac{1}{2}(84\text{cm}\times12\text{cm})=504\text{cm}^2$
Hence, Area of quadrilateral ABCD = Area of ADC + Area of ABC
$=(693+504) cm ^2=1197 cm^2$
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