Related Skills

► Area and perimeter Sums

► Geometry sums

► Four sided Figures

1) PQRS is a four-sided piece of paper. Triangle PQS is folded downwards along line QS to form the shaded part Triangle QST. Given that QS = 8 cm, TU = 3 cm and ST = TR, find the area of the figure PQRS.

Ans :- Area of figure PQRS is 36 cm²

2) The figure below consists of two overlapping squares ABCD and BXYZ. Q is the ^{1}⁄_{5} mark of the sides, DC and ZY. Express the shaded area as a fraction of the total unshaded area. (Give your answer in its simplest form)

Ans :- ^{1}⁄_{8}

3) Tommy noticed the patterns on the square tiles and tried to calculate the area of the shaded part. (Take π = 3.14)

Ans :- The area of shaded part is 218.88 cm²

4) Triangle ABC is an isoseles triangle. 2 simmilar semi-circles are cut out from the triangle as shown in the diagram. The radius of the semi-circle is 10 cm. Find the area of the Black part.

Take π = 3.14.

Ans :- The area of the Black part is 21.5 cm².

5) The figure below shows 3 different recangles, A, B and C. 20% of rectangle A and 30% of rectangle C is shaded. The shaded area of A is the same as the shaded area of C. What fraction of the figure is shaded if 40% of rectangle B is shaded?

Ans :- ^{3}⁄_{17} of the figure is shaded.

6) The figure below is formed by using a quadrant and two simmilar semi-circles of diameter 6 cm. Find the perimeter of the shaded part. (Take π = 3.14

Ans :- The perimeter of the shaded part is 49.68 cm

7) The figure below shows 3 semi-circles. Given that CD is half of BD and BD is half of AD, find the total area of the shaded parts when the radius of the smallest semi-circle is 1 cm. (Leave your answer in terms of π)

Ans :- The total area of shaded parts is 6½π cm²

8) The figure below is made up of a square of side 28 cm. One semi-circle and one quadrant are drawn inside the square.

Given that the total area of portion A and C is two times the area of B, find the area of B. (Take π = 22/7)

Ans :- The area of B is 119 cm²

9) In the right angled triangle below, the two sides which forms the right angle are 16 cm and 12 cm respectively. 4 such triangles are arranged to form a big square as shown. Find the perimeter of the big square.

Ans :- Perimeter of the big square is 80 cm.

10) The figure is made up of 4 identical circles with a diameter of 14 cm. Find the area of the shaded region. (Take π = 3.14)

Ans :- The area of shaded region is 111.72 cm²