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Area and perimeter Sums
Geometry sums
Four sided Figures

Math worksheet for Area and Perimeter

1) The figure below, not drawn to scale, is made up of a square, a rectangle and an isosceles triangle. Find the area of the shaded part.

Ans :- 114 cm².

2) The figure consists of 3 over-lapping shapes, a circle (X), an equilateral triangle (Z) and a rectangle (Y). The ratio of the area of X to the area of Y to the area of Z is 2 : 3 : 5 and the shaded area of X to the shaded area of Z is 1 : 3. If the ratio of the shaded area of Z is 1 : 3. If the ratio of the shaded area of Z to unshaded area of Z is 1 : 4, what is the ratio of the total shaded area to the total unshaded area?

Ans :- 2 : 11.

3) A1, A2 and A3 are triangles not drawn to scale. The area of A1 is 25% of A2 and the area of A2 is 64% of A3.
a) What is the ratio of the area of A1 to A2 to A3? Express the answer in its simplest form.
b) When the area of A1 is enlarged, the area becomes 20% of the area of A3. What is the percentage increase in the area of A1?

Ans :- a) 4 : 16 : 25
b) 25% .

4) The figure below shows a square of side 15 cm with a semicircle and 2 quadrants inside. Find the difference between the shaded P and Q. Express your answer to the nearest 2 decimal places.
(Take  = 3.14)

Ans :- 39.94 cm².

5) The figure below is not drawn to scale. The perimeter of the shaded rectangle is 14 cm. A square is drawn on each side of the shaded rectangle is 14 cm. A square is drawn on each side of the shaded rectangle and they are labelled A, B, C and D. The total area of the 4 squares is 58 cm².
What percentage of the area of square A is the area of square B?

Ans :- 16%.

6) The figure shows 4 small identical circles in a big circle. The small circle is of radius 14 cm and the big circle is of diameter 70 cm.
(a) Find the shaded area.
(b) Find the perimeter of the unshaded part marked X which is enclosed by the four smaller circles. (Take π = 227 )

Ans :- a) 1218 cm²
b) 88 cm .

7) A toy maker has a rectangular block of wood, 30 cm by 14 cm by 10 cm, as shown in Figure 1. He cuts as many 3-cm cubes as possible from the block of wood and is left with the L-shaped block of wood as shown in Figure 2.

(a) How many 3-cm cubes can he cut?
(b) What is the total area of the faces of the remaining L-shaped block of wood?

Ans :- a) 120 cubes can be cut
b) 1504 cm² .

8) In the diagram below, the area of the rectangle ABCD is 40 cm². P, Q and R are the mid points of AB, BC and CD respectively. S is a point on AD. Find the area of the shaded parts .

Ans :- 20 cm².