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# Arithmetic Aptitude :: Area

Home > Arithmetic Aptitude > Area > General Questions

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1. A 16 stored building has 12000 sq. feet on each floor. Company A rents 7 floors and company B rents 4 floors. What is the number of sq. feet of unrented floor space.

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Explanation:

Given 16 floors building which each floor has 12000 sq.ft
so total space = 16*12000 is 192000.
11 floors are given for rent so 11*12000 ie 132000
so the unrented floor space is (192000-132000) = 60000

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2. If 12 file cabinets require 18 feet of wall space, how many feet of wall space will 30 cabinets require?

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Explanation:

12 files cabinates require wall space = 18 feet.
Assume 30 cabinates it require = x feet.
=> 12x = 30*18
=> x=45

by chain rule

12                 18
30 (D)           x (D)
30/12 = x/18 => 30/12 * 18 = 45

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3. The dimensions of a certain machine are 48" X 30" X 52". If the size of the machine is increased proportionately until the sum of its dimensions equals 156", what will be the increase in the shortest side?

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Explanation:

48+30+52=130, then 156-130=26

the "proportionately" in the shortest side means 30/130*26=6"

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4. A hollow space on earth surface is to be filled. Total cost of filling is Rs20000. The cost of filling per mt3 is Rs 225 .how many times a size of 3 mt3 soil is required to fill the hollow space?

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Explanation:

20000/225=88.88
88.88/3=29.62 .So 30 times of 3 mt3 is required to fill the space completely.

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5. 4 horses are tethered at 4 corners of a square plot of side 63 meters so that they just cannot reach one another. the area left ungrazed is

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Explanation:

area of square = 63*63=3969 m^2
area inside the square that is grazed =4*area of quadrants of 4 circles
= 4*(1/4)*(22/7)*(63/2)*(63/2) =3118.5
area left ungrazed = 3969-3118.5=850.5

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6. What is the percentage of increase in area of a triangle if its sides are doubled?

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Explanation:

In similar triangles, a ratio of areas is equal to a ratio of the square of corresponding sides.

Area 2/Area 1 = (side 2/side 1)²

When sides are doubled, the area of the new triangle will always be 4 times the original, the change in area will be 3 times. Hence the % change will always be 300% irrespective of the type of triangle.

In similar triangles, a ratio of areas is equal to a ratio of the square of corresponding sides.

Area 2/Area 1 = (side 2/side 1)²

When sides are doubled, the area of the new triangle will always be 4 times the original, the change in area will be 3 times. Hence the % change will always be 300% irrespective of the type of triangle.

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7. A square and an equilateral triangle have the same perimeter. What is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle?

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Explanation:

let x be side of square
perimeter of square=4x=perimeter of triangle=3*side of triangle
so side of eq. triangle=(4/3)*x
diameter of circle circumscribing the square=sqrt(2)*x
area of circle circumscribing the square=pi*(sqrt(2)*x)^2/4=(pi/2)*x^2 ----(1)
to find radius of the circle inscribed in the triangle
area of triangle=r*s=sqrt(3)/4 * (4x/3)^2
now s=(4/3)*x+(4/3)*x+(4/3)*x/2=2x
so sqrt(3)/4 * (4x/3)^2=r*2x gives
r={2/3*(3^1/2)}*x
area of the circle inscribed in the triangle=pi*({2/3*(3^1/2)}*x)^2
=pi*(4/27)*x^2 -------(2)
so reqd ratio= eqn(1)/eqn(2)
=((pi/2)*x^2)/(pi*(4/27)*x^2)=27/8
so reqd ratio=27:8

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8. Sky Heaven is a 16 stored building with 12000 sq. feet on each floor. Zintac International rents 7 floors and Zobia International rents 4 floors. What is the number of sq. feet of unrented floor space?

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Explanation:

total floors = 16
rented floors = 7 + 4 = 11
unrented floors = 16-11=5
no. of sq. feet = 5 * 12000= 60000 sq. feet

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9. A builder has to pour a concrete slab 12 centimeters thick to cover an area 10 meters long and 2 meters wide. How many cubic meters of concrete will the builder need?

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Explanation:

Given Thickness of the slab = 12cm.= 0.12m.
Given area is 10m. long and 2m wide.
Total concrete needed =the volume of the area = (0.12 * 10 * 2)= 2.4 cubic meter.

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10. There is a rectangular Garden whose length and width is 60m X 20m.There is a walkway of uniform width around garden. Area of walkway is 516m^2. Find width of walkway?

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Explanation:

Lets assume width of rectangle = x m.
So new length will be (60+2x) and width (20+2x)
Area of walkway = 516m^2
=> (60+2x)*(20+2x)-(60*20)=516.
=> (60+2x)*(20+2x)=1716.
=> (30+x)*(10+x)=429
=> x=3m

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