## Area and Perimeter

#### Area and Perimeter

1. Area of a square is 1/2 hectare. The diagonal of the square is?
1. 250 meter
2. 100 meter
3. 50√ 2 meter
4. 50 meter

1. Area = 1/2 hectare = 10000 / 2 m2
= 5000 m2

Again Area = 1/2 x (Diagonal)2

##### Correct Option: B

Area = 1/2 hectare = 10000 / 2 m2
= 5000 m2

Again Area = 1/2 x (Diagonal)2

So 1/2 x (Diagonal)2 = 5000m2
⇒ Diagonal2= 10000
∴ Diagonal = 100

1. The base of right-angled triangle is 5 meters and hypotenuse is 13 meters . Its area will be ?
1. 25m2
2. 28 m2
3. 30m2
4. None of these

1. Altitude = √(13)2 - (5)2
= √144 = 12m

##### Correct Option: C

Altitude = √(13)2 - (5)2
= √144 = 12m

∴ Area of the triangle = (5 x 12 ) / 2 m2
= 30m2

1. The length of a rectangle is double while its breadth is halved. What is the percentage change in area ?
1. 50
2. 75
3. No change
4. None of these

1. Let length = l and breadth = b
Then, area = lb

New length = 2l
∴ New area = ( 2l ) x (b/2) = lb

##### Correct Option: C

Let length = l and breadth = b
Then, area = lb

New length = 2l
∴ New area = ( 2l ) x (b/2) = lb

So, there is no change in area .

1. The cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paisa per meter is Rs. 36. The breadth of the room is ?
1. 6 meters
2. 8 meters
3. 9 meters
4. 12 meters

1. Length of carpet = Total Cost / Rate
= 3600 / 30
= 120 m

Area of carpet = (120 x 75) / 100 m2
= 90 m2
∴ Area of the room = 90 m2

##### Correct Option: A

Length of carpet = Total Cost / Rate
= 3600 / 30
= 120 m

Area of carpet = (120 x 75) / 100 m2
= 90 m2
∴ Area of the room = 90 m2

Breadth of the room = Area /Length
= 90 / 15 m
= 6m

1. If the side of a square is increased by 25%, then how much percent does its area get increased ?
1. 125
2. 156.25
3. 50
4. 56.25

1. Let area 100 m2
Then, side = 10 m

New side = 125 % of 10
= (125/100) x 10)
= 12.5 m

New area = 12.5 x 12.5 m2
=(12.5)2 sq. m

##### Correct Option: D

Let area 100 m2
Then, side = 10 m

New side = 125 % of 10
= (125/100) x 10
= 12.5 m

New area = 12.5 x 12.5 m2
=(12.5)2 sq. m

∴ Increase in area = (12.5)2 - (10)2 m2
= 22.5 x 2.5 m2
=56.25 m2

% Increase = 56.25 %