Question : ABCD is a quadrilateral. The length of the diagonal AC is 24 cm. The sum of the perpendicular drawn from vertex B and D on the diagonal AC is 10 cm. What is the area of the quadrilateral?
Option 1: 240 cm2
Option 2: 180 cm2
Option 3: 120 cm2
Option 4: 90 cm2
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Correct Answer: 120 cm 2
Solution :
Given: $d=24$ cm and $h_1+h_2=10$ cm.
The area of the quadrilateral $=\frac{1}{2}\times(h_1+h_2)\times d$ where $d$ and $(h_1+h_2)$ are its diagonals and sum of heights.
So, the area $=\frac{1}{2}\times10\times 24=120$ cm
2
Hence, the correct answer is 120 cm
2
.
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