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) cm

Answer 1

Let a = area of one small triangle. The hexagon is made of 6 such triangles, so b = 6a. The entire shaded region is all 12 triangles, so its area is 12a.

Using b = 6a, the equivalent expressions are:
- 12a
- 2b (since 2b = 2·6a = 12a)
- 6a + b (since 6a + b = 6a + 6a = 12a)

So select: 12a cm2, 2b cm2, and (6a + b) cm2.