Question

the diagram shows a regular pentagon with side length s. explore the area of this pentagon by following these steps
√ 1. press continue to partition the pentagon into five congruent triangles.
√ 2. press continue to draw an apothem with length a.

1. based on the variables on the diagram, how can the area of the shaded triangle be determined?

area =

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).

Step2: Identify the base and height of the shaded triangle

In the shaded triangle, the base is \(s\) (the side - length of the pentagon) and the height is \(a\) (the apothem).
Substitute the base \(b = s\) and height \(h=a\) into the area formula: \(A=\frac{1}{2}\times s\times a=\frac{1}{2}sa\).

Answer:

\(\frac{1}{2}sa\)