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 length of a rectangle is 10 cm more than the breadth. Find the diagonal length of rectangle if perimeter is 44 cm ?

A) 12.50 cm B) 14.21 cm
C) 15.98 cm D) 17.08 cm
 
Answer & Explanation Answer: D) 17.08 cm

Explanation:

Let the length of the rectangle = L cm

 

Then the breadth of the rectangle = (L - 10) cm

 

Perimeter of a rectangle = 2(L + B) cm

 

=> 44 = 2(L + L - 10)

 

=> 44 = 4L - 20

 

=> 4L = 64

 

=> L = 16 cm

 

=> B = L - 10 = 6 cm

 

Diagonal = L2+B2 = 162+62 = 17.08 cm

Report Error

View Answer Report Error Discuss

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

11 4078
Q:

The number of diagonals in a decagon is:

 

A) 20 B) 10
C) 25 D) 35
 
Answer & Explanation Answer: D) 35

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

0 3991
Q:

The area of a square is equal to the area of a rectangle. The length of the rectangle is 5 cm more than a side of the square and its breadth is 3 cm less than the side of the square. What is the perimeter of the rectangle ? 

A) 15 cm B) 18 cm
C) 34 cm D) 26 cm
 
Answer & Explanation Answer: C) 34 cm

Explanation:

Let the side of the square be 's' cm

 

length of rectangle = (s+5) cm

 

breadth of rectangle = (s-3)cm

 

(s+5) (s-3) = 

 

s2 - 5s - 3s - 15 = s2 

 

2s = 15

 

Perimeter of rectangle = 2(L+B) = 2(s+5 + s–3) = 2(2s + 2)

 

= 2(15 + 2) = 34 cm 

Report Error

View Answer Report Error Discuss

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

28 3940
Q:

The perimeter of a square is 26 cm. Find its area (in cm2).

 

A) 42.25   B) 84.5  
C) 39.25   D) 78.5
 
Answer & Explanation Answer: A) 42.25  

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

0 3911
Q:

 

If LMN and UVW are similar triangles, the value of side s is

A) 4 B) 6
C) 8 D) 9
 
Answer & Explanation Answer: C) 8

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

0 3874
Q:

The area of an equilateral triangle is 16√3 sq.cm. Find its side in cm.

 

A) 8 B) 4
C) 16 D) 24
 
Answer & Explanation Answer: A) 8

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

0 3792
Q:

∆ABC is right angled at B. If cosA = 8/17, then what is the value of cotC ?

 

A)  15/8 B) 15/17
C)  8/17 D) 17/15
 
Answer & Explanation Answer: A)  15/8

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

1 3763
Q:

The area of an equilateral triangle is 49√3 cm2. Find its side (in cm).

 

A) 7 B) 14
C) 28 D) 42
 
Answer & Explanation Answer: B) 14

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

0 3755