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:

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

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Q:

In the given figure, PQRSTU is a regular hexagon of side 12 cm. What is the area (in sq.cm) of triangle SQU?

A) 162√3 B) 216√3
C) 108√3 D) 54√3
 
Answer & Explanation Answer: C) 108√3

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3 1645
Q:

In the given figure, four identical semicircles are drawn in a quadrant. XA = 7 cm. What is the area (in sq.cm) of shaded region ?

 

A) 70 B) 140
C) 77 D) 84
 
Answer & Explanation Answer: D) 84

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Q:

The area of a regular hexagon is equal to the area of the square. What is the ratio of the perimeter of the regular hexagon to the perimeter of square?

A) 63 : 36 B) 23 : 62
C) 63 : 2 D) 63 : 23
 
Answer & Explanation Answer: D) 63 : 23

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0 1626
Q:

In the given figure, ABCDEF is a regular hexagon of side 12 cm. P, Q and R are the mid points of the sides AB, CD and EF respectively. What is the area (in sq.cm) of triangle PQR?

A) 27√6 B) 81√3
C) 54√3 D) 54√6
 
Answer & Explanation Answer: B) 81√3

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Q:

A cube is placed inside a cone of radius 20 cm and height 10 cm, one of its face being on the base of the cone and vertices of opposite face touching the cone. What is the length (in cm) of side of the cube?

A) 5 B) 6
C) 8 D) 9
 
Answer & Explanation Answer: C) 8

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Q:

In the circle above, chord AB is extended to meet the tangent DE at D. If AB = 12 cm and DE = 8 cm, find the length of BD.

A) 4 cm B) 5 cm
C) 6 cm D) 7 cm
 
Answer & Explanation Answer: A) 4 cm

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4 1605
Q:

The length of the radius of the circumference of a triangle having sides 9 cm, 12 cm and 15 cm is

A) 6 cm B) 7.5 cm
C) 4.5 cm D) 8 cm
 
Answer & Explanation Answer: B) 7.5 cm

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