Question

In this diagram, ABAC – AEDF. If thearea of ABAC = 6 in2, what is thearea of AEDF?DAE 2 inB3 inс=Area = [? ] in2Enter a decimal rounded to the tenths.a

Answer 1

Area of ΔBAC = 6 in^2

EF = 2 in

BC = 3 in

Both triangles are similar, so:

Area ΔBAC : Area of ΔEDF = BC^2 : EF^2

Replacing:

6 / Area of ΔEDF = 3^2 / 2^2

Cross multiply

6 * 2^2 = 3^2 * Area of ΔEDF

24 = 9 * Area of ΔEDF

24/9 = Area of ΔEDF

Area of ΔEDF = 8/3 in^2 = 2.7 in^2