# Pythagorean Theorem Word Problems

### Solutions

1A 10 m long ladder is leaning against a wall. The bottom of the ladder is 6 m from the base of where the wall meets the ground. At what height from the ground does the top of the ladder lean against the wall?

2Determine the side of an equilateral triangle whose perimeter is equal to a square of side 12 cm. Are their areas equal?

3Calculate the area of an equilateral triangle inscribed in a circle of radius 6 cm.

4Determine the area of the square inscribed in a circle with a circumference of 18.84 cm.

5A square with a side of 2 m has a circle inscribed in it and in turn this circle has a square inscribed in it. If this square also has a circle inscribed in it, what is the area between the last square and the last circle.

6The perimeter of an isosceles trapezoid is 110 m and the bases are 40 and 30 m in length. Calculate the length of the non-parallel sides of the trapezoid and its area.

7A regular hexagon of side 4 cm has a circle inscribed and another circumscribed around its shape. Find the area enclosed between these two concentric circles.

8A chord of 48 cm is 7 cm from the center of a circle. Calculate the area of the circle.

9The legs of a right triangle inscribed in a circle measure 22.2 cm and 29.6 cm. Calculate the circumference and the area of the circle.

10A central angle of 60° is plotted on a circle with a 4 cm radius. Calculate the area of the circular segment between the chord joining the ends of the two radii and its corresponding arc.

## 1

A 10 m long ladder is leaning against a wall. The bottom of the ladder is 6 m from the base of where the wall meets the ground. At what height from the ground does the top of the ladder lean against the wall?

## 2

Determine the side of an equilateral triangle whose perimeter is equal to a square of side 12 cm. Are their areas equal?

P_{square} = 12 · 4 = 48 cm

P_{triangle} = 48 cml = 48 : 3 = 16 cm

A = 12^{2} = 144 m²

## 3

Calculate the area of an equilateral triangle inscribed in a circle of radius 6 cm.

The center of the circle is the centroid. Therefore:

## 5

A square with a side of 2 m has a circle inscribed in it and in turn this circle has a square inscribed in it. If this square also has a circle inscribed in it, what is the area between the last square and the last circle.

## 6

The perimeter of an isosceles trapezoid is 110 m and the bases are 40 and 30 m in length. Calculate the length of the non-parallel sides of the trapezoid and its area.

## 7

A regular hexagon of side 4 cm has a circle inscribed and another circumscribed around its shape. Find the area enclosed between these two concentric circles.

## 9

The legs of a right triangle inscribed in a circle measure 22.2 cm and 29.6 cm. Calculate the circumference and the area of the circle.

A triangle inscribed whose diameter coincides with the hypotenuse is always a right triangle.

## 10

A central angle of 60° is plotted on a circle with a 4 cm radius. Calculate the area of the circular segment between the chord joining the ends of the two radii and its corresponding arc.