FACTS  AND  FORMULAE  FOR  AREA  QUESTIONS

 

 

FUNDAMENTAL CONCEPTS :

I. Results on Triangles:

1. Sum of the angles of  a triangle is 180o

2. The sum of any two sides of a triangle is greater than the third side.

3. Pythagoras Theorem : In a right - angled triangle,

Hypotenuse2=Base2+Height2

4. The line joining the mid-point of a side of a triangle to the opposite vertex is called the median.

5. The point where the three medians of a triangle meet, is called Centroid. The centroid divides each of the medians in the ratio 2 : 1.

6. In an Isosceles triangle, the altitude from the vertex bisects the base.

7. The median of a triangle divides it into two triangles of the same area.

8. The area of the triangle formed by joining the mid-points of the sides of a given triangle is one-fourth of the area of the given triangle.

 

II.Results on Quadrilaterals :


1. The diagonals of a parallelogram bisect each other

2. Each diagonal of a parallelogram divides it into two triangles of the same area.

3. The diagonals of a rectangle are equal and bisect each other.

4. The diagonals of a square are equal and bisect each other at right angles

5. The diagonals of a rhombus are unequal and bisect each other at right angles

6. A parallelogram and a rectangle on the same base and between the same parallels are equal in area.

7. Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.

 

IMPORTANT FORMULAE

I. 

1. Area of a rectangle = (length x Breadth)

Length =AreaBreadth  and  Breadth=AreaLength

2. Perimeter of a rectangle = 2( length + Breadth)

 

 

II. Area of square = side2=12diagonal2 

 

III. Area of 4 walls of a room = 2(Length + Breadth) x Height

 

 

IV.

1. Area of a triangle =12×base×height

2. Area of a triangle = s(s-a)(s-b)(s-c), where a, b, c are the sides of the triangle and s=12a+b+c

3. Area of an equilateral triangle =34×side2

4. Radius of incircle of an equilateral triangle of side a=a23

5. Radius of circumcircle of an equilateral triangle of side a=a3

6. Radius of incircle of a triangle of area  and semi-perimeter s=s

 

 

V.

1. Area of a parallelogram = (Base x Height)

2. Area of a rhombus = 12×Product of diagonals

3. Area of a trapezium = 12×(sum of parallel sides)×distance between them

    

 

VI.

1. Area of a cicle = πR2, where R is the radius.

2. Circumference of a circle = 2πR.

3. Length of an arc = 2πRθ360, where θ is the central angle.

4. Area of a sector = 12arc×R=πR2θ360 

 

VII.

1. Area of a semi-circle = πR22

2. Circumference of a semi - circle = πR

Q:

The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

A) 16 B) 18
C) 20 D) 22
 
Answer & Explanation Answer: B) 18

Explanation:

2l+bb=51      => 2l + 2b = 5b     => 3b = 2l 

b=(2/3)l

 

Then, Area = 216 cm2 

=> l x b = 216     => l x (2/3)l =216 

l = 18 cm.

Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams
Job Role: Bank PO

43 51425
Q:

A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 75 paise per sq m is

A) Rs. 258 B) Rs. 358
C) Rs. 458 D) Rs. 558
 
Answer & Explanation Answer: D) Rs. 558

Explanation:

Area to be plastered = 2l+b×h+l×b 

=225+12×6+25×12=744sq.m 

Cost of plastering = 744×75100=Rs.558                       

Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams
Job Role: Bank PO

78 46264
Q:

The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

A) 20% B) 30%
C) 40% D) 50%
 
Answer & Explanation Answer: D) 50%

Explanation:

Let original length = x and original breadth = y.

Original area = xy. 

New length = x/2 and New breadth=3y 

New area = 32xy 

Therefore,  Increase in area = New area-original area = 32xy-xy=12xy 

 

Therefore,  Increase % = increase in area original area*100=12xyxy*100=50 %

Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams
Job Role: Bank PO

47 45385
Q:

A parallelogram has sides 30m and 14m and one of its diagonals is 40m long. Then its area is

A) 136 B) 236
C) 336 D) 436
 
Answer & Explanation Answer: C) 336

Explanation:

let ABCD be the given parallelogram 

area of parallelogram ABCD = 2 x (area of triangle ABC) 

now a = 30m, b = 14m and c = 40m

 s=1/2 x (30+14+40) = 42 

 

Area of triangle ABC = ss-as-bs-c  

 

= 4212282= 168sq m 

area of parallelogram ABCD = 2 x 168 = 336 sq m

Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams
Job Role: Bank PO

103 44395
Q:

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) 1.04 B) 2.04
C) 3.04 D) 4.04
 
Answer & Explanation Answer: D) 4.04

Explanation:

100 cm is read as 102 cm. 

A1 = (100*100)Sq.cm 

A2 = (102*102)Sq.cm

(A2 - A1) = 1022-1002 = (102 + 100) x (102 - 100) = 404 sq.cm.

Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams
Job Role: Bank PO

40 44279
Q:

The length of a rectangle is twice its breadth if its length is decreased by 5cm and breadth is increased by 5cm, the area of the rectangle is increased by 75 sq cm. Find the length of the rectangle.

A) 30 B) 40
C) 50 D) 60
 
Answer & Explanation Answer: B) 40

Explanation:

let length = 2x and breadth = x then
(2x-5) (x+5) = (2x * x)+75
5x-25 = 75 => x=20
length of the rectangle = 40 cm

Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams
Job Role: Bank PO

51 41665
Q:

A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be

A) 7744 B) 8844
C) 5544 D) 4444
 
Answer & Explanation Answer: A) 7744

Explanation:

length of wire = 2πr= 2 x (22/7 ) x 56 = 352 cm
side of the square = 352/4 = 88cm
area of the square = 88 x 88 = 7744sq cm

Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams
Job Role: Bank PO

77 41381
Q:

The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750 sq.m. The length of the hall is

A) 20 B) 25
C) 30 D) 35
 
Answer & Explanation Answer: C) 30

Explanation:

Let breadth = x m

 

Then, length = (x+5)m

 

Area of a rectangle = Length x Breadth

 

x(x+5) = 750 

 

x² + 5x - 750= 0

 

(x+30)(x-25)= 0

 

x = 25 or x = -30

 

Hence, breadth x = 25m

 

=> Length = x + 5 = 25 + 5 = 30m. 

Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk , Analyst

71 41353