Question

writing an expression for the shaded regions. an equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon. write an expression for the area of the shaded regions. shaded area = area of the - area of the + area of the - area of the. equilateral triangle, square, regular hexagon

Explanation:

Step1: Understand area - subtraction principle

The shaded area is found by subtracting the non - shaded areas from the outer - most shape's area.

Step2: Identify the outer - most and inner shapes

The outer - most shape is the regular hexagon and the inner shapes (non - shaded) are the square and equilateral triangle. The regular pentagon's area is part of the shaded region.

Step3: Write the expression

Shaded area = area of the regular hexagon - area of the square+ area of the regular pentagon - area of the equilateral triangle

Answer:

Shaded area = area of the regular hexagon - area of the square+ area of the regular pentagon - area of the equilateral triangle