ABCD is a quadrilateral with diagonal $BD = 70 ext{ cm}$. Perpendiculars from vertices $A$ and $C$ to diagonal $BD$ are $AL = 18 ext{ cm}$ and $CM = 20 ext{ cm}$ respectively. Find the area of quadrilateral $ABCD$.

Question

ABCD is a quadrilateral with diagonal $BD = 70 	ext{ cm}$. Perpendiculars from vertices $A$ and $C$ to diagonal $BD$ are $AL = 18 	ext{ cm}$ and $CM = 20 	ext{ cm}$ respectively. Find the area of quadrilateral $ABCD$.

Accepted Answer

**Solution:**

1. Given diagonal $BD = 70 	ext{ cm}$.

2. Perpendiculars from vertices $A$ and $C$ to diagonal $BD$ are $AL = 18 	ext{ cm}$ and $CM = 20 	ext{ cm}$ respectively.

3. The formula for the area of the quadrilateral when perpendiculars from opposite vertices to a diagonal are given:

$$	ext{Area} = \frac{1}{2} 	imes BD 	imes (AL + CM)$$

4. Substitute the values:

$$	ext{Area} = \frac{1}{2} 	imes 70 	imes (18 + 20) = 35 	imes 38 = 1330 	ext{ cm}^2$$

**Answer:** $1330 	ext{ cm}^2$

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