Grade 7 Maths Mensuration Quiz (Part A)

The length of a rectangle is 16 cm and the length of its diagonal is 20 cm. The area of the rectangle is

Answer explanation

To find the area of the rectangle, use the formula: Area = length * width. Since the diagonal, length, and width form a right triangle, we can use Pythagorean theorem to find the width. Width = sqrt(diagonal^2 - length^2) = sqrt(20^2 - 16^2) = 12 cm. Therefore, Area = 16 cm * 12 cm = 192 cm^2.

 Each diagonal of a square is 12 cm long. Its area is

• none of these

Answer explanation

The area of a square is half the product of the diagonals. Therefore, the area is (1/2) * 12 * 12 = 72 cm^2. Hence, the correct answer is 72 cm^2.

• 10 cm

• 20 cm

• 14.1 cm

Answer explanation

The correct choice is 20 cm. The diagonal of a square can be found using the formula: diagonal = side * sqrt(2). Given the area is 200 cm^2, the side length is 10 cm. Therefore, the diagonal is 10 * sqrt(2) = 20 cm.

The area of a square field is 0.5 hectare. The length of its diagonal is

• 100 m

• 50 m

• 
  250 m

Answer explanation

The correct answer is 100 m. The diagonal of a square can be found using the formula: diagonal = side * sqrt(2). Given the area is 0.5 hectare, we can find the side length, which is 100 m. Therefore, the diagonal is 100 m.

The length of a rectangular field is thrice its breadth and its perimeter is 240 m. The length of the field is

• 80 m

• 120 m

• 90 m

• none of these

Answer explanation

The correct length of the rectangular field can be calculated by solving the equation 2x + 2(3x) = 240, where x represents the breadth. Therefore, the length is 90 m.

The length of a rectangular field is thrice its breadth and its perimeter is 240 m. The length of the field is

• 80 m

• 120 m

• 90 m

• none of these

Answer explanation

The correct length of the rectangular field can be calculated by solving the equation 2x + 2(3x) = 240, where x represents the breadth. Therefore, the length is 90 m.

On increasing each side of a square by 25%, the increase in area will be

• 25 %

• 55 %

• 40.5 %

• 56.25%

Answer explanation

On increasing each side of a square by 25%, the area increases by (1.25)^2 = 1.5625, which is equivalent to 56.25% increase.

The ratio of the area of a square to that of the square drawn on its diagonal is :

Answer explanation

The correct ratio is 1:2 because the area of a square is half the area of the square drawn on its diagonal.

Answer explanation

The correct statement is A > B because if the perimeters are equal, the square will have a larger area than the rectangle.

The length and breadth of a rectangular field are in the ratio 5 : 3 and its perimeter is 480 m. The area of the field is

Answer explanation

The correct answer is 13500 m^2. To find the area, we first calculate the length and breadth using the ratio. Then, we use the formula for the area of a rectangle: length * breadth.