Pythagorean Theorem Worksheet

Solutions

1Given an equilateral triangle with a side of 6 cm, find the area of the circular sector determined by the circle circumscribed around the triangle and the radius passing through the vertices.

2Calculate the area enclosed by the inscribed and circumscribed circles to a square with a diagonal of 8 m in length.

3If non-parallel sides of an isosceles trapezoid are prolonged, an equilateral triangle with sides of 6 cm would be formed. Knowing that the trapezoid is half the height of the triangle, calculate the area of the trapezoid.

4The area of a square is 2,304 cm². Calculate the area of a regular hexagon that has the same perimeter as this square.

5A square is inscribed in a circle of 4 m radius and on the sides of the square are outward pointing equilateral triangles. Calculate the area of this shape.


1

Given an equilateral triangle with a side of 6 cm, find the area of the circular sector determined by the circle circumscribed around the triangle and the radius passing through the vertices.

The center of the circle is the centroid. Therefore:

Radius Formula

Circular Sector Problem

Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Solution


2

Calculate the area enclosed by the inscribed and circumscribed circles to a square with a diagonal of 8 m in length.

Concentric Circles Problem

Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Operations

Pythagorean Theorem Operations

Pythagorean Theorem Solution


3

If non-parallel sides of an isosceles trapezoid are prolonged, an equilateral triangle with sides of 6 cm would be formed. Knowing that the trapezoid is half the height of the triangle, calculate the area of the trapezoid.

 

Area of a Trapezoid Problem

Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Solution


4

The area of a square is 2,304 cm². Calculate the area of a regular hexagon that has the same perimeter as this square.

 

Area of a Hexagon Problem

Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Operations

Pythagorean Theorem Operations

Pythagorean Theorem Solution


5

A square is inscribed in a circle of 4 m radius and on the sides of the square are outward pointing equilateral triangles. Calculate the area of this shape.

Area Word Problem

Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Operations

Pythagorean Theorem Solution