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Area and perimeter Sums
Geometry sums
Four sided Figures

Math worksheet for Area and Perimeter

1) In the figure PQRS is a rectangle.
The areas of triangles PXQ, PXS and XSR are 144.5 cm², 44.5 cm² and 122.25 cm² respectively. Find the area of triangle XSQ.

Ans :- 78.11 cm² .

2) The figure below is made of a semicircle, a quadrant and a square. The area of the square is 784 cm². Find the total area of the shaded parts. Express your answer to 2 decimal places.

Ans :- 588.00 cm² .

3) In the figure below, KL is the arc of a quarter circle. Use the calculator value of π to find the total area of the shaded parts. Correct your answer to 1 decimal place.

Ans :- 195.9 cm² .

4) The figure below shows a semicircle and a right-angled triangle ABC. The lengths of AB and BC are 19 cm and 27.5 cm respectively. The area of the shaded region X is 92 cm² more than the area of the shaded region Y. Find the diameter of the semicircle. (Take π = 3.14)

Ans :- 30 cm.

5) The figure below is made up of a rectangle and a square. The ratio of the area of the rectangle to the area of the square is 5 : 2. After the shaded part is cut out, the ratio of the unshaded part of the rectangle to the unshaded part of the square becomes 3 : 1. Given that the length of the square is 6 cm, find the area of the shaded part.

Ans :- 9 cm².

6) The figure is made up of square ABCD and two circles. The radius of each circle is 6 cm. Find the area of the shaded region.
(Take π = 3.14)

Ans :- 61.56 cm².

7) The diagram is made up of 3 circles. OC, the radius of the smallest circle, is 2 cm. OE is the radius of the medium-size circle and OF is the radius of the biggest circle.
(a) What is the ratio of the area of the smallest circle to the area of the biggest circle?
(b) Find the area of the shaded part. (Leave your answer to the nearest 2 decimal places)

Ans :- a) 1 : 16
b) 150.80 cm² .

8) In the diagram not drawn to scale, AB = 6 cm, CD = 12 cm, ED = 8 cm, AF = 5 cm and ∠AFE and ∠BCD = 90°. Find the shaded area.

Ans :- 56 cm².

9) The figure below, not drawn to scale, is made up of 2 squares. There are quadrants within the squares. AB and BC are straight lines. Find the total shaded area. Correct your answer to 1 decimal place.
(Take π = 3.14)

Ans :- 315.3 cm².

10 The figure below, not drawn to scale, shows a square and a rectangle that are overlapping each other.
The area of the square to the area of the rectangle is 2 : 5.
The ratio of the area of the square to the area of the shaded part
is 5 : 2.
If the shaded area is 10 cm², find the area of the unshaded part of the figure.

Ans :- 67.5 cm².