Question

For quadrilateral ABCD with AC ⊥ BD , find the area using the information in the pictures below. Derive a formula for the area of a quadrilateral with perpendicular diagonals using the diagonals only.

ANSWER: The numeric value of area is __ sq units

**FIRST CORRECT ANSWER GETS BRAINLIEST ANSWER*

Answer 1

Area of triangle ABD = $\frac{b \times h}{2}$

Area of triangle ABD = $\frac{(10+20) \times 15}{2}$

Area of triangle ABD = $\frac{30 \times 15}{2}$

Area of triangle ABD = (15) (15) = 225 sq. units

Area of triangle BDC = $\frac{b \times h}{2}$

Area of triangle BDC = $\frac{(10+20) \times 25}{2}$

Area of triangle BDC = $\frac{30 \times 25}{2}$

Area of triangle BDC = (15) (15) = 375 sq. units

Area of Quadrilateral ABCD = Area of triangle ABD + Area of triangle BDC

Area of Quadrilateral ABCD = 225 + 375 = 600 sq. units

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BD = d1 and AC = d2

Area of triangle ABD = $\frac{b \times h}{2}$

Area of triangle ABD = $\frac{d1 \times AO}{2}$

Area of triangle BDC = $\frac{b \times h}{2}$

Area of triangle BDC = $\frac{d1 \times OC}{2}$

Area of Quadrilateral ABCD = Area of triangle ABD + Area of triangle BDC

Area of Quadrilateral ABCD = $\frac{d1 \times AO}{2}$ + $\frac{d1 \times OC}{2}$

Area of Quadrilateral ABCD = $\frac{1}{2}\times d1(AO + OC)$

But AO + OC = AC = d2

Area of Quadrilateral ABCD = $\frac{1}{2}\times d1 \times d2$