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?

Psquare = 12 · 4 = 48 cm

Ptriangle = 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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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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