Mensuration Quiz

The area of a square is numerically equals six times its perimeter. Determine twice its side length.

1. 8 cm
2. 24 cm
3. 48 cm
4. 52 cm

Answer: (c) 48 cm

The sum of the areas of two triangles is 146 cm². The area of one triangle is 34 cm² more than that of the other triangle. If the ratio of the height of the smaller triangle to the height of the larger triangle is 4 : 3, then determine the ratio of their corresponding bases.

1. 7 : 45
2. 15 : 7
3. 28 : 45
4. 7 : 15

Answer: (d) 7 : 15

The cost of fencing a rectangular plot at the rate of $100 per metre is $y. Given that the breadth of the rectangular plot is a cm. Which of the following represents the length of the rectangle?

1. (y - 2a)/100 m
2. (2y - a)/100 m
3. (y - 2a)/200 m
4. (y - a)/200 m

Answer: (c) (y - 2a)/200 m

In the given figure, O is the center of the circle and BC = 10 cm. Determine the difference between the shaded region and the unshaded region. (Use π = 3.14)

1. 25 cm²
2. 28.5 cm²
3. 53.5 cm²
4. 78.5 cm²

Answer: (b) 28.5 cm²

What is the cost of fencing a square park with an area of 64 m² at the rate of $1,100 per 20 m?

1. $1,760
2. $6,050
3. $60,500
4. $17,600

Answer: (a) $1,760

A rectangular room measuring 42 m x 40 m is to be completely covered using 105 square tiles of equal size. What is the perimeter of each tile?

1. 8 m
2. 4 m
3. 16 m
4. 20 m

Answer: (c) 16 m

Peter owns a square park with a side length of 32 m. At the center of the park is a circular pond whose radius is 2 m less than half the side of the park. Peter plans to plant grass in the remaining area of the park, excluding the pond, at a cost of $155 per 10 square metres. Calculate the total amount Peter will need. (Use π = 22/7)

1. $6,324
2. $9,548
3. $15,872
4. $63,240

Answer: (a) $6,324

In the given figure, ABC is an isosceles triangle and ABCD is a square. It is given that AB = AC, AB = 6 cm and AF = 12 cm. If the area of △ABC is 108 cm², Determine the perimeter of the given figure.

1. 36 cm
2. 42 cm
3. 60 cm
4. 48 cm

Answer: (b) 42 cm

A rectangular garden measures 20 m in length and 15 m in breadth. A uniform path, 2 m wide, is constructed all around the garden. Calculate the area of the path.

1. 156 m²
2. 74 m²
3. 300 m²
4. 456 m²

Answer: (a) 156 m²

The perimeter of a rectangle is equal to that of a square. If the breadth of the rectangle is half its length, find a relationship between S and R, where S is the area of the square and R is the area of the rectangle.

1. R = 9S/32
2. 8R = 9S
3. S = 9R
4. 9R = 8S

Answer: (d) 9R = 8S