Examples with solutions for Area of a Trapezoid: 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

Below is the trapezoid ABCD.

AB = 5 cm

DC = 10 cm

EC = 2 cm

AF = 4 cm
AF is perpendicular to DC.

Calculate the area of the quadrilateral ABCE.

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Video Solution

Answer

14

Exercise #3

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 #4

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