Question

The 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 small triangles, so b = 6a. The whole figure has 12 triangles, area = 12a. Using b = 6a gives 12a = 2b and 12a = 6a + b, so the three equivalent expressions are 12a, 2b, and (6a + b).