Question 1

The diagonals of two squares are in the ratio of 2:5. Find the ratio of their areas.

Accepted Answer

let the diagonals of the squares be 2x and 5x respectively ratio of their areas = 1 2 * 2 x 2 : 1 2 * 5 x 2 = 4:25

Question 2

If the area of a square with side a s equal to the area of a triangle with base a, then the altitude of the triangle is

Accepted Answer

Area of a square with side a = a² sq unts Area of a triangle with base a = (1/2) * a * h sq.unts a² =1/2 *a *h => h = 2a altitude of the triangle is 2a

Question 3

Find the perimeter and area of a square that has a side of length 14 feet.

Accepted Answer

Perimeter of a square p=4s ,where s=length of its side => p=4(14)=56 feets Area of a square A = s x s => A=196 The perimeter is 56 feet, and the area is 196 square feet.

Question 4

If a parallelogram with area p, a triangle with area R and a triangle with area T are all constructed on the same base and all have the same altitude, then

Accepted Answer

let each have base = b and height = h then p = b*h, R = b*h and T = (1/2) * b*h so P = R, P = 2T and T = (1/2)*R are all correct statements

Question 5

A man walked diagonally across a square plot. Approximately what was the percent saved by not walking along the edges?

Accepted Answer

let the side of the square be x meters length of two sides = 2x meters diagonal = 2 x = 1.414x m saving on 2x meters = .59x m saving % = 0 . 59 x 2 x * 100 % = 30% (approx)

Question 6

The area of a rectangle is 80 cm.If its length is 16 cm, what is its width?

Accepted Answer

A=LB

Question 7

The area of a square is 49 mm. What is the length of each side?

Accepted Answer

A = S 2

Question 8

Find the area of the rectangle or square with the given dimensions s=10 feet

Accepted Answer

A = S 2

Question 9

A wheelchair slalom event, athletes weave around cones and race to the finish line. A diagram of the rectangular course 30m length &16m bredth is shown. Find the the area of the course

Accepted Answer

A = lw

Question 10

Area of circle is equal to the area of a rectangle having perimeter of 50 cms. and length more than the breadth by 3 cms. What is the diameter of the circle?

Accepted Answer

Let the breadth of rectangle be x cm => Length of rectangle = (x+3) cm Now, perimeter =2(x+x+3) = 50 => 2x + 3 = 25 => x = 11 Thus, breadth = 11 cm and length = 14 cm Area of circle = Area of rectangle =>pi * r* r = 14 * 11 =>r*r = 14 * 11 * 7/22 =>r = 7 cm Diameter = 2 * 7 = 14 cm

Question 11

There is a square field of area ‘X’ square meters. A cylindrical ditch of radius 7 meters and depth 2 meters is dug, and the earth is taken out and spread over the remaining part of the square field, the height of square field which goes up by 0.77 …

Accepted Answer

Volume of the cylindrical ditch = πrxrh = 22/7 ×7×7×2 = 308 sq.m Area of remaining field = (X −πrxr) sq.m = (X − 154) ATQ – (X – 154) ×0.77 = 308 (X – 154) = 400 X= 554 sq.m

Area Questions