1. Anthony had 3 rectangular pieces of cardboard. He cut out 3 semicircles, each with a diameter of 14 cm from the cardboard. The perimeter of the remaining piece of cardboard as shown below is 154 cm. What is the length of XY? (Take π = 22⁄7)
Ans :- Length of XY is17 cm.
2. Jack bought some candies that came in a square pyramid as shown in the figure below. Each pyramid has a square base area of 1 cm² and a vertical height of 1 cm.
He then packed the candies in a box measuring 6 cm by 4 cm by 4 cm. What was the maximum number of such candies that he could pack into the box?
Ans :- He could pack 176 such candies.
3. The figure below, not drawn to scale, shows a rectangle, ABCD, which is divided into 4 parts, W, X, Y and Z.
The ratio of the area of W to the area of X is 1 : 3.
The ratio of the area of X to the area of Y is 2 : 7.
If the area of Z is 238 cm², what is the area of rectangle ABCD?
Ans :- the area of rectangle ABCD is 644 cm².
4. In the figure below, the length of the square is 1⁄3 the bredth of the rectangle.
(a) What is the length of the square in terms of n.
(b) What is the area of the shaded part when n = 3?
Ans :- a) the length of the square is 2n cm
b) The area of the shaded part is 450 cm².
5. The figure below is made up of three squares.
(a) Express the perimeter of the figure in terms of y.
(b) The area of each of the small squares is 4 cm². Find the area of the whole figure.
Ans :- a) 20y cm
b) 72 cm².
6. One large and two small quadrants are drawn in a square as shown. Find the area of the part that is coloured. (Take π = 3.14)
Ans :- 56.76 cm².
7. The figure comprises of a circle and a square. The ratio of the area of the yellow region to the area of the blue region is 1 : 4. The perimeter of the square is 20 cm. The circumference of the circle is 44 cm. Find the total area of the red, yellow and blue parts.
Ans :- 174 cm².
8. If the green triangle is greater than the yellow triangle by 9 cm², find the breadth of the rectangle.
Ans :- 5 cm.
9. Find the area of the shaded parts. Take π = 22⁄7
Ans :- 112 cm².
10. The area of ∆ABE is 16 cm². smaller than ∆CDE. Find AB.
Ans :- AB = 6 cm.