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:

Point P is the midpoint of segment AB. Co-ordinates of P are (3 , 1) and B are (5, -4). What are the co-ordinates of point A?

A) (-1 , 7) B) (1 , -7)
C) (1 , 6) D) (-1 , -7)
 
Answer & Explanation Answer: C) (1 , 6)

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Q:

Two equal circles intersect so that their centres, and the points at which they intersect form a square of side 1 cm. The area (in sq.cm) of the portion that is common to the circles is

A) π4 B) π2-1
C) π5 D) √2 - 1
 
Answer & Explanation Answer: B) π2-1

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Q:

If the cost of 17 m of cloth is Rs. 77 5/7, find its cost per meter in Rs.?

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

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Q:

In ΔDEF measure of angle E is 90°. If cosD = 8/17, and DE = 16cm, then what is the length (in cm) of side DF?

 

A) 30 B) 20
C) 26 D) 34
 
Answer & Explanation Answer: D) 34

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Q:

What is the area (in sq cm) of a rectangle if its diagonal is 26 cm and one of its sides is 10 cm?

A) 120 B) 240
C) 360 D) 480
 
Answer & Explanation Answer: B) 240

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Q:

What is the area (in sq cm) of a rectangle if its diagonal is 25 cm and one of its sides is 24 cm?

A) 186 B) 144
C) 132 D) 168
 
Answer & Explanation Answer: D) 168

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Q:

What is the area (in sq cm) of a rectangle of perimeter 48 cm and breadth 10 cm?

A) 140 B) 480
C) 240 D) 440
 
Answer & Explanation Answer: A) 140

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Q:

In a triangle PQR, ∠PQR = 90 deg, PQ = 10 cm and PR = 26 cm, then what is the value (in cm) of inradius of incircle?

A) 9 B) 4
C) 8 D) 6
 
Answer & Explanation Answer: B) 4

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