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:

In the given figure, ABCD is a square of side 14 cm. E and F are mid points of sides AB and DC respectively. EPF is a semicircle whose diameter is EF. LMNO is a square . What is the area (in sq.cm) of the shaded region?

 

A) 108.5 B) 94.5
C) 70 D) 120
 
Answer & Explanation Answer: B) 94.5

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Q:

A rectangular swimming pool of length 20 m and breadth 10 m has a uniformly sloping floor. It is 1 m in depth on one end of its length and 3 m at the other. How much water is needed to completely fill this pool? (Take π = 22/7)

A) 800 cubic metres B) 300 cubic metres
C) 480 cubic metres D) 400 cubic metres
 
Answer & Explanation Answer: D) 400 cubic metres

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0 903
Q:

The area of a triangle with vertices A (0, 8) , O (0,0) and B (5, 0) is:

A) 8 sq. units B) 13 sq. units
C) 20 sq. units D) 40 sq. units
 
Answer & Explanation Answer: C) 20 sq. units

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2 902
Q:

The measures of the four angles of a quadrilateral are in the ratio 1:2:3:4. What is the measure of the biggest angle?

A) 36° B) 144°
C) 72° D) 108°
 
Answer & Explanation Answer: B) 144°

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0 899
Q:

In ΔABC, the angle bisector of ∠A cuts BC at E. Find the length of AC if lengths of AB, BE and EC are 9.6 cm, 4 cm and 3 cm?

A) 4.8 cm B) 9.8 cm
C) 7.8 cm D) 7.2 cm
 
Answer & Explanation Answer: D) 7.2 cm

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0 897
Q:

The area of a square is 72.25 cm². Find its perimeter (in cm).

A) 68 B) 44
C) 34 D) 88
 
Answer & Explanation Answer: C) 34

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0 896
Q:

Find the area (in sq units) enclosed by y = 0, x+6=0 and 2x-3y=6.

A) 9 B) 16
C) 20 D) 27
 
Answer & Explanation Answer: D) 27

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5 894
Q:

A rectangular swimming pool of length 30 m and breadth 15 m has a uniformly sloping floor. It is 1 m in depth on one end of its length and 2 m at the other. How much water is needed to completely fill this pool?

A) 1350 cubic mts B) 2025 cubic mts
C) 675 cubic mts D) 2700 cubic mts
 
Answer & Explanation Answer: C) 675 cubic mts

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0 889