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:

ABCDEF is a regular hexagon of side 12 cm. What is the area (in cm2) of the triangle ECD?

A) 18√3 B) 24√3
C) 36√3 D) 42√3
 
Answer & Explanation Answer: C) 36√3

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2 1044
Q:

The length and breadth of a rectangle is in the ratio of 3 : 1. If its perimeter is 96 m, then what is the length of the rectangle?

A) 36m B) 24m
C) 12m D) 48m
 
Answer & Explanation Answer: A) 36m

Explanation:

Let the length of the rectangle be 3x and breadth be 1x
Given, perimeter = 96 m
2(l + b) = 96 (or) l + b = 48 (or) 3x + 1x = 48 (or) x = 12 m
Now, Length of the rectangle = 12 x 3 = 36 m

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3 1023
Q:

What is the length of the arc whose central angle is 30° and radius of the circle is 21 cm?

A) 22 cm B) 16.5 cm
C) 11 cm D) 28 cm
 
Answer & Explanation Answer: C) 11 cm

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1 1019
Q:

The area of a circle is 616 sq cm, find its circumference?

A) 44 cm B) 88 cm
C) 22 cm D) 176 cm
 
Answer & Explanation Answer: B) 88 cm

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4 1008
Q:

A quadrilateral is inscribed in a circle. If the opposite angles of the quadrilateral are equal and length of its adjacent sides are 6 cm and 8 cm, what is the area of the circle?

A) 64π sq cm B) 25π sq cm
C) 36π sq cm D) 49π sq cm
 
Answer & Explanation Answer: B) 25π sq cm

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4 1008
Q:

What is the length of the side of a regular hexagon, if its area is 54√3 sq cm?

A) 12 cm B) 9 cm
C) 6 cm D) 15 cm
 
Answer & Explanation Answer: C) 6 cm

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1 1005
Q:

If the radius of a circle is decreased to 25% of its original value, calculate the percentage decrease in the area of the circle

A) 25% B) 43.75%
C) 50% D) 93.75%
 
Answer & Explanation Answer: D) 93.75%

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1 1005
Q:

In the given figure, two squares of sides 8 cm and 20 cm are given. What is the area (in sq.cm) of the shaded part?

A) 120/7 B) 160/7
C) 180/7 D) 240/13
 
Answer & Explanation Answer: B) 160/7

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