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 perimeters of a square and an equilateral triangle are equal. If the diagonal of the square is 9 cm, what is the area of the equilateral triangle?

A) 18√3 sq cm B) 9√3 sq cm
C) 18√2 sq cm D) 9√2 sq cm
 
Answer & Explanation Answer: A) 18√3 sq cm

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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 1420
Q:

x, y be two acute angles, x + y < 90° and sin(2x - 20°) = cos(2y + 20°), the value of tan(x + y) is

A) √3 B) 1/√3
C) 1 D) 2+√2
 
Answer & Explanation Answer: C) 1

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Q:

Find the greatest length which can be used to measure exactly three cloth pieces of lengths 1.26 m, 1.98 m and 1.62 m respectively.

A) 12 cm B) 14 cm
C) 16 cm D) 18 cm
 
Answer & Explanation Answer: D) 18 cm

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0 1417
Q:

ΔPQR is right angled at Q. QS is the altitude. PQ is 2√13 cm and PS is 8 cm. What is the length of SR?

A) 6√13 cm B) 4√13 cm
C) 18 cm D) 9 cm
 
Answer & Explanation Answer: C) 18 cm

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Q:

Length and breadth of a rectangle are increased by 40% and 70% respectively. What will be the percentage increase in the area of rectangle?

A) 118 B) 110
C) 138 D) 128
 
Answer & Explanation Answer: C) 138

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1 1412
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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0 1410
Q:

Δ LMN is right angled at M. If m∠N = 45°, what is the length of MN (in cm), if NL = 9√2 cm?

A) 9√2 B) 9/√2
C) 18 D) 9
 
Answer & Explanation Answer: D) 9

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