Use Area to Solve Problems Quick Check

Question

4 of 54 of 5 Items

Question
Use the image to answer the question.

An illustration shows a composite figure of two similar sets where a central pentagon is surrounded by a layer of 5 pentagons, one on each side. Two central pentagons are drawn separately with dashed lines. On each side of the central pentagons, another pentagon is drawn using solid lines. Each central pentagon has 5 surrounding pentagons. One pentagon from each set shares a common side.

A net that folds into a dodecahedron is made up of pentagons. If you decompose each pentagon into one triangle and one trapezoid, how many triangles and how many trapezoids are there?

Answer 1

Each pentagon can be decomposed into one triangle and one trapezoid.

Since there are 5 pentagons in each set, there are 5 triangles and 5 trapezoids in each set.

Therefore, in total for the two similar sets, there are 10 triangles and 10 trapezoids.