Question

AABC and AEBF are similar triangles. What is the area of AEBF in sq units? A(12.14) (a,6) E 11 (3,2) B F C (12,2)​

Answer 1

Answer:

12 ÷ 14 = 0.8571

0.8571 × 11(3 +2)

11 × 5 =55

47.1405 × 14= 659.967 ×0.8571

=565.7

Answer 2

Given:

ΔEDF ~ΔABC

To Find:

The area of Δ EDF in square units.

Solution:

If ΔABC and ΔEDF are similar triangles to each other, then the ratio of the area of a triangle is equal to the square of the ratios of their corresponding sides

So, area(ΔABC)/area(ΔEDF) = (AB/ED)² = (BC/DF)² = (CA/FD)²

This can also be written as,

area(ΔABC)/area(ΔDEF) = (AB/DE)²

Area of ΔABC is given as 144cm² and DE = 27cm, AB = 36cm

Substituting the given values in,

area(ΔABC)/area(ΔDEF) = (AB/DE)²

⇒ 144/area(ΔDEF) = (36/27)²

⇒ 144/x = (36/27)²

⇒ 144/x = √36/27

⇒ 144/x = 3/2

Taking the reciprocal of the whole equation

areaΔDEF = 3/2 × 144

                 = 216cm²

Therefore, the area of triangle DEF = 216cm².