You are given a right triangle, quadrilateral and pentagon with equal sides a. You need to find the ratio of areas

We write down the area formulas for each of the figures, the area of ​​an equilateral triangle is expressed by the formula:

S = a² * √3 / 4;

The area of ​​a regular quadrangle, that is, the area of ​​a square:

S = a²; since a regular quadrangle is a square;

The area of ​​a regular pentagon (pentagon) is expressed by the formula:

S = a² * √ (25 + 10 * √5) / 4.

To calculate the ratio of the areas of these figures, we rewrite them and shorten their right parts:

(a² * √3 / 4) / a² / (a² * √ (25 + 10 * √5) / 4) = (√3 / 4) / 1 / (√ (25 + 10 * √5) / 4), since it is possible to shorten these expressions by a².

We calculate this ratio in numerical value, rounded to two decimal places, we get the ratio:

(1.73 / 4): 1: (6.88 / 4) = 0.43: 1: 1.72.

Answer: The areas of a triangle, square and pentagon relate to each other as 0.43: 1: 1.72 (rounded).