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:

A square ground is to be covered by planting 100 saplings on each side. How many saplings are needed in all?

 

A) 400 B) 404
C) 396 D) 408
 
Answer & Explanation Answer: C) 396

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Q:

Consider the circle shown below having angle AOB as 135 deg and the shaded portion is the x part of the circular region. Calculate the value of x.

 

A) 1/12 B) 1/9
C) 1/6 D) 1/4
 
Answer & Explanation Answer: D) 1/4

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Q:

The order of rotational symmetry of a trapezium is

A) 2 B) 0
C) 1 D) 3
 
Answer & Explanation Answer: C) 1

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Q:

The length of one side and the diagonal of a rectangle are 20 cm and 29 cm respectively. Find the length of its other side (in cm).

 

A) 42   B) 30  
C) 21   D) 60
 
Answer & Explanation Answer: C) 21  

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Q:

If the measure of the interior angle of a regular polygon is 120 deg then how many sides does it have?

 

A) 6 B) 8
C) 9 D) 10
 
Answer & Explanation Answer: A) 6

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Q:

The length of one side and the diagonal of a rectangle are 8 cm and 17 cm respectively. Find its area (in cm2).

 

A) 240   B) 120  
C) 80   D) 160
 
Answer & Explanation Answer: B) 120  

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Q:

The number of sides of a regular polygon whose exterior angles are each 60 deg is

A) 7 B) 5
C) 6 D) 8
 
Answer & Explanation Answer: C) 6

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Q:

An angle is 60 deg more than one fifth of its complement. Find the smaller angle in degrees.

A) 65 deg B) 35 deg
C) 25 deg D) 45 deg
 
Answer & Explanation Answer: C) 25 deg

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