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 the two parallel sides of a trapezium are 16 m and 20 m respectively. If its height is 10 m, its area in square metres is

A) 360 B) 260
C) 240 D) 180
 
Answer & Explanation Answer: D) 180

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Q:

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:3 and area of ΔADE is 4 sq cm, what is the area (in sq cm) of quadrilateral BDEC.

A) 25 B) 21
C) 5 D) 9
 
Answer & Explanation Answer: B) 21

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Q:

The two equal sides of an isosceles triangle is 20 cm each and the third side is 30 cm. What is the area(in cm2) of the triangle?

A) 50√5 B) 100
C) 75√7 D) 175
 
Answer & Explanation Answer: C) 75√7

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Q:

What is the area (in sq cm) of a circle whose circumference is 22 cm?

A) 77 B) 38.5
C) 44 D) 88
 
Answer & Explanation Answer: B) 38.5

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Q:

In the given figure, ABCD is a square whose side is 4 cm. P is a point on the side AD. What is the minimum value (in cm) of BP + CP ?

A) 4√5 B) 4√4
C) 6√3 D) 4√6
 
Answer & Explanation Answer: A) 4√5

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Q:

The slopes of two lines are 1/√3 and √3. What is the angle between these two lines?

A) 15° B) 45°
C) 60° D) 30°
 
Answer & Explanation Answer: D) 30°

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Q:

Area of _____ equals square of its side.

A) Rhombus B) Cyclic quadrilateral
C) Rectangle D) Square
 
Answer & Explanation Answer: D) Square

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Q:

Δ DEF is right angled at E. If m ∠D = 30°. What is the length (in cm) of DE, if EF = 2√3 cm?

A) 3 B) 4
C) 6 D) 2
 
Answer & Explanation Answer: C) 6

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