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:

Which of the following represents the sides of an acute angled triangle?

 

A) 6, 9, 16   B) 7, 8, 10  
C) 5, 12, 13   D) None of these
 
Answer & Explanation Answer: B) 7, 8, 10  

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

0 1863
Q:

Find the circumference (in cm) of a circle of radius 7 cm.

 

A) 56 B) 44
C) 16 D) 32
 
Answer & Explanation Answer: B) 44

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

2 1795
Q:

Length and breadth of a rectangle are 8 cm and 6 cm respectively. The rectangle is cut on its four vertices such that the resulting figure is a regular octagon. What is the side (in cm) of the octagon?

A) 3(√11) – 7 B) 5(√13) – 8
C) 4(√7) – 11 D) 6(√11) – 9
 
Answer & Explanation Answer: A) 3(√11) – 7

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

3 1776
Q:

For the figure given below, find the angle OAB (in degrees).

 

A) 25 B) 50
C) 75 D) 90
 
Answer & Explanation Answer: C) 75

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

1 1776
Q:

If the radius of a circle is increased by 25%, its area increases by:

A) 50 percent B) 25 percent
C) 28.125 percent D) 56.25 percent
 
Answer & Explanation Answer: D) 56.25 percent

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

4 1732
Q:

In the given figure, PQRS is a rectangle and a semicircle with SR as diameter is drawn. A circle is drawn as shown in the figure. If QR = 7 cm, then what is the radius (in cm) of the small circle ?

 

A) 21 + 14√2 B) 21 – 14√2
C) Both 21 + 14√2 and 21 – 14√2 D) None of these
 
Answer & Explanation Answer: B) 21 – 14√2

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

1 1700
Q:

In the given figure, ,PQRS is a square whose side is 8 cm. PQS and QPR are two quadrants. A circle isplaced touching both the quadrants and the square as shown in the figure. What is the area (in sq.cm) of the circle?

A) 13/17 B) 11/14
C) 19/31 D) 15/19
 
Answer & Explanation Answer: B) 11/14

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

2 1655
Q:

What is the measure of an exterior angle of a regular polygon of 6 sides?

 

A) 45 deg B) 60 deg
C) 40 deg D) 36 deg
 
Answer & Explanation Answer: B) 60 deg

Explanation:
Report Error

View Answer Report Error Discuss

Filed Under: Area
Exam Prep: Bank Exams

0 1649