Examples with solutions for Area of a Circle: Subtraction or addition to a larger shape

Exercise #1

A trapezoid is shown in the figure below.

On its upper base there is a semicircle.

What is the area of the entire shape?

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Video Solution

Answer

24+3.125π 24+\text{3}.125\pi cm².

Exercise #2

Two circles share a center point, marked O.

What is the area of the shaded part of the orange circle?

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Video Solution

Answer

12π 12\pi cm²

Exercise #3

Look at the circle in the figure.

Its center is O.

Inside the circle there is a square.

What is the area of the white parts combined?
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Video Solution

Answer

23.085 cm²

Exercise #4

From the point O on the circle we take the radius to the point D on the circle. Given the lengths of the sides in cm:

DC=8 AE=3 OK=3 EK=6

EK is perpendicular to DC

Calculate the area between the circle and the trapezoid (the empty area).

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Video Solution

Answer

36.54

Exercise #5

The trapezoid ABCD is drawn inside a circle.

The radius can be drawn from point O to point C.

DC = 12 cm
OK = 3 cm
NB = 4 cm
NK = 5 cm

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Calculate the white area between the trapezoid and the circle's edge.

Video Solution

Answer

91.37

Exercise #6

Look at the rectangle in the figure.

A semicircle is added to each side of the rectangle.

What is the area of the entire shape?

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Video Solution

Answer

32+20π 32+20\pi cm².

Exercise #7

The drawing shows an equilateral triangle

The length of each of its sides 7 cm

a semicircle is placed on each side of each side

What is the area of the entire shape? Replace π=3.14 \pi=3.14

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Video Solution

Answer

78.91 cm².