Question

Find the area of the given quadrilateral ABCD, given that the length of BD, AE and BC are 28 cm, 12 cm, and 8 cm respectively and AE and BC are perpendiculars from vertices A and C respectively.

• A. 280 $c{m}^2$
• B. 340 $c{m}^2$
• C. 320 $c{m}^2$
• D. None of these

Answer 1

The correct option is A

280 $c{m}^2$

It is given that DB = 28 cm, AE = 12 cm and BC = 8 cm

AE and BC are perpendiculars from vertices A and C respectively
AE and BC are perpendicular to diagonal BD
Area of quadrilateral ABCD = Area of $\Delta$ ABD + Area of $\Delta$ BDC
= $\frac{1}{2}$ $\times$ DB $\times$ AE + $\frac{1}{2}$ $\times$ DB $\times$ BC

[Area of triangle = Half the product of the base and height.]
= $\frac{1}{2}$ $\times$ DB $\times$ (AE + BC)
= $\frac{1}{2}$ $\times$ 28 $\times$ (12 + 8)
= 280 $c{m}^2$