Question

he figure consists of 12 congruent equilateral triangles. The area of one equilateral triangle is a cm2. The area of the hexagon, shaded slightly darker, is b cm2.

A figure is comprised of 12 congruent equilateral triangles. A hexagon is formed by 6 triangles. The area of the 6 triangle is shaded slightly darker.

Which expressions represent the area of the entire shaded region, including the light and dark shading? Select three options.

12a cm2
2b cm2
(6a – b) cm2
(12a + 2b) cm2
(6a + b) cm2

Answer 1

Answer: 12a, 2b, and (6a + b).

Reason: the hexagon is made of 6 congruent triangles so b = 6a. The entire shaded region is all 12 triangles, area = 12a. Substituting b = 6a gives 2b = 2(6a) = 12a and 6a + b = 6a + 6a = 12a, so those three expressions are equivalent. The other two are not.