Related Skills

► Area and perimeter Sums

► Geometry sums

► Four sided Figures

1. The plot of land shown in the figure is made up of 2 squares and a triangle. It has an area of 198 cm². If the area of the small square is twice the area of the triangle, find the perimeter of the plot of land.

Ans :- 56.5 cm.

2. A yellow rectangle is painted in a square as shown below. The area of the blue region is 80 cm². If EB is twice the as long as AE, find the area of the square.

Ans :- 144 cm².

3. The rectangular block shown below has a volume of 960cm³. The area of the face painted green is 96 cm². If the ratio of its length to its height is 3 : 2, find its base area.

Ans :- 120 cm².

4. The figure below shows a circle enclosed in a square. The square has an area of 100 cm². What is the circumference of the circle? (Express your answer to 1 decimal place.)

Ans :- The circumference of the circle is 31.4 cm.

5. The diagram shows a square inside a circle with a radius of 10 cm. Find the shaded area.

Ans :- 114 cm².

6. The figure below shows a square and 4 identical circles with diameter of 20 cm each. Find the area of the shaded part. (Give your answer correct to 2 decimal places)

Ans :- The area of shaded part is 228.32 cm²

7. The figure is made up of one circle, 4 semicircles and a triangle.

O is the centre of the circle. AB is 28cm. Find the total area of the shaded part. (Take π = ^{22}⁄_{7} )

Ans :- The area of shaded part is 168 cm²

8. A piece of wire is bent to form 6 similar semi-circles as shown in the figure below. If the area of the enclosed rectangle is 200cm². Find the length of the piece of wire. (Take π = 3.14)

Ans :- The length of the piece of wire is 94.2 cm

9. The figure below is made up of three triangles A, B and C.

50% of Triangle A is shaded

¼ of Triangle B is shaded.

20% of Triangle C is shaded

The total area of Triangle A and Triangle B is 125% of the area of Triangle C. Express the area of Triangle A as a fraction of the area of Triangle B.

Leave your answer in its simplest form.

Ans :- ^{3}⁄_{22}.

10. The figure below is made up of a triangle and a rectangle.
The ratio of the area of the triangle to the area of the rectangle is 9 : 20.
The shaded area is ^{4}⁄_{9} of the area of the triangle.
The unshaded area is 126 cm². Find the area of the triangle.

Ans :- The area of the triangle is 54 cm².