Formulae
1. Area of a rectangle = (Length x Breadth).
2. Length = Area/Breadth and Breadth = Area/Length
3. Perimeter of a rectangle = 2(Length + Breadth)
4. Area of a square = (side)2 = 1/2(diagonal)2.
5. Area of 4 walls of a room = 2 (Length + Breadth) x Height
6. Area of a triangle = 1/2x Base x Height.
7. Area of parallelogram = (Base x Height).
8. Area of a rhombus = 1/2x (Product of diagonals).
9. Area of a trapezium = 1/2x (sum of parallel sides) x distance between them.
| Figures | Formula | Variables |
| Rectangle | Area = l | l = length w = width |
| Square | Area = | a = sides of square |
| Triangle | Area = | b = base h = height |
| Circle | Area = | r = radius of circle |
| Trapezoid | Area = | a = base 1 b = base 2 h = vertical height |
| Ellipse | Area = | a = radius of major axis b = radius of minor axis |
Exercise : Area MCQ Questions and Answers
Question 1
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
| A. |
| B. |
| C. |
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Correct Answer : A. 4.04%
Description :
100 cm is read as 102 cm.
∴ A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = ( \( {404 \over {100 x 100}} \) x 100 ) % = 4.04%
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Question 2
The area of a triangle is with base 4m and height 5m?
| A. |
| B. |
| C. |
| D. |
Correct Answer : A. 10 m2
Description :
Area of a triangle = 1/2x Base x Height
1/2 * 4 * 5 = 10 m2
Question 3
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
| A. |
| B. |
| C. |
| D. |
Correct Answer : C. 153600 m2
Description :
Question seems to be typical, but trust me it is too easy to solve, before solving this, lets analyse how we can solve this.
We are having speed and time so we can calculate the distance or perimeter in this question.
Then by applying the formula of perimeter of rectangle we can get value of length and breadth, So finally can get the area. Lets solve it:
Perimeter = Distance travelled in 8 minutes,
=> Perimeter = 12000/60 * 8 = 1600 meter. [because Distance = Speed * Time]
As per question length is 3x and width is 2x
We know perimeter of rectangle is 2(L+B)
So, 2(3x+2x) = 1600
=> x = 160
So Length = 160*3 = 480 meter
and Width = 160*2 = 320 meter
Finally, Area = length * breadth
=480*320=153600 m2