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?

Right Triangle



Pythagorean Theorem Exercise

 

2

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

Psquare = 12 · 4 = 48 cm

Ptriangle = 48 cml = 48 : 3 = 16 cm

Square



A = 122 = 144 m²

Triangle Problem


Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Solution


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:

Pythagorean Theorem Exercise

Equilateral Triangle

formulas

Pythagorean Theorem Operations

Pythagorean Theorem Solution


4

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

Square Inscribed in Circle

Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Solution


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.


Circles Inscribed in Squares

Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Operations

Pythagorean Theorem Operations

Pythagorean Theorem Operations

Pythagorean Theorem Solution


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.

 

Isoscles Trapezoid

Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Solution


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.

 

Concentric Circles around a Hexagon

Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Solution


8

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

 

Area of a Circle

Pythagorean Theorem Exercise

Pythagorean Theorem Solution


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.

Triangle Inscribed in a Circle

Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Solution


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.

 

Circular Segment

Pythagorean Theorem Exercise

Pythagorean Theorem Operations

Pythagorean Theorem Operations

Pythagorean Theorem Solution