Chapters

- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
- Solution of exercise 1
- Solution of exercise 2
- Solution of exercise 3
- Solution of exercise 4
- Solution of exercise 5
- Solution of exercise 6
- Solution of exercise 7
- Solution of exercise 8
- Solution of exercise 9
- Solution of exercise 10

## Exercise 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?

## Exercise 2

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

## Exercise 3

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

## Exercise 4

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

## Exercise 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.

## Exercise 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.

## Exercise 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.

## Exercise 8

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

## Exercise 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.

## Exercise 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.

## Solution of exercise 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?

## Solution of exercise 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 = 12² = 144 m²

## Solution of exercise 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:

## Solution of exercise 4

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

## Solution of exercise 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.

## Solution of exercise 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.

## Solution of exercise 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.

## Solution of exercise 8

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

## Solution of exercise 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.

## Solution of exercise 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.

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