Question : What will be the area of a plot of quadrilateral shape, one of whose diagonals is 20 m and lengths of the perpendiculars from the opposite vertices on it are 12 m and 18 m, respectively?
Option 1: 400 m2
Option 2: 250 m2
Option 3: 200 m2
Option 4: 300 m2
Correct Answer: 300 m 2
Solution :
Given: The diagonals are 20 m and the lengths of the perpendiculars from the opposite vertices on it are 12 m and 18 m, respectively.
Use the formula, $\text{Area of the triangle}=\frac{1}{2}\times \text{Base}\times \text{Height}$.
The area of the $\triangle ABC=\frac{1}{2}\times \text{AC}\times \text{BO}=\frac{1}{2} \times 20\times 12=120$ m
2
.
The area of the $\triangle ADC=\frac{1}{2}\times \text{AC}\times \text{DP}=\frac{1}{2}\times 20\times 18=180$ m
2
.
The area of a plot of quadrilateral shape = 180 + 120 = 300 m
2
Hence, the correct answer is 300 m
2
.
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