Question

The rectangle shown has length AC = 32, width

AE = 20, and B and F are midpoints of AC and AE , respectively. The area of quadrilateral ABDF is:

A. 320 B. 325 C. 330 D. 335 E. 340

Answer 1

A. 320

Explanation:

See attachment for the figure

in order to determine Area of quadrilateral ABDF, we'll use the formula i.e

Area of quadrilateral ABDF = Area of AECD - Area of ΔBCD - Area of ΔDEF ->eq(1)

whereas, area of AECD = (AC × AE)

Area of ΔBCD = 1/2 (BC x CD)

Area of ΔDEF =1/2 ( EF x ED)

Substituting in eq(1)

eq(1)=>

Area of quadrilateral ABDF = (AC × AE) - 1/2 (BC x CD)- 1/2 ( EF x ED)

=(32 x 20) - 1/2(16 x 20) - 1/2(10 x 32)

= 640 - 160 - 160

= 640 - 320

= 320 square unit

Therefore, the area of quadrilateral ABDF is 320 square unit