# NCERT Class 9 Physics Herons Formula Formative Assessment CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. Calculate the area in each case

a) Triangle have sides as a = 5 cm, b = 4 cm, c = 3 cm

Solution:

Area

b) Equilateral triangle having side a = 2 cm

Solution:

b) Area of equilateral

c) Right angle triangle have base = 4 cm and Height = 3 cm

Solution:

c) Area of triangle

d) Square whose diagonal is 10 cm?

Solution:

d) Area of square in terms diagonal

e) Rectangle whose length and breath are 6 and 4 cm

Solution:

e) Rectangle area is given by

f) Parallelogram whose two sides are 10 cm and 16 cm and diagonal is 14 cm

Solution:

f) In parallelogram whose two sides and diagonal are given, Area is given by

Where s =

So

g) Parallelogram whose base is 10 cm and height is 14 cm

Solution:

g) Area is given by

h) Rhombus of diagonals to 10 and 24 cm

Solution:

h) Area is given by

i) Two sides of trapezium are 36 and 24cm and its altitude is 12cm.

Solution:

i) Area of trapezium is given by

A = Altitude (Sum of parallel sides)

**2) True or False statement**

a) Heron formula for area of triangle is not valid of all triangles

Solution: False

b) If each side of the triangles is tripled, the area will becomes 9 times

Solution: True

c) Base and corresponding altitude of the parallelogram are 8 and 5 cm respectively. Area of parallelogram is

Solution: True

d) If each side of triangle is doubled, the perimeter will become 4 times

Solution: False

e) If p is the perimeter of the triangle of sides a, b, c, the area of triangle is

Solution: True

f) When two triangles are congruent, there areas are same

Solution: True

g) Heron՚s belongs to America

Solution: False

h) If the side of the equilateral triangle is a rational number, the area would always be irrational number

Solution: True

Multiple choice Questions

3) The difference between sides at right angles in a right angled triangle is 14 cm. The area of the triangle is 120 . The perimeter of the triangle is

a) 80

b) 45

c) 60

d) 64

Solution (c)

Let y be one of the at right angle, then another side will be y-14

Now we know that

So other side is 10

From pythogrous theorem

Hypotenuse

So perimeter will be

4. Find the area of the equilateral triangle whose perimeter is 180 cm?

Which of the following is true?

a)

b)

c)

d) None of these

Solution

Area of equilateral

5) One diagonal and side of the rhombus are 24 and 13 cm respectively, find the Area and other diagonal size?

a)

b)

c)

d) None of the above

Solution (c)

Solution a

BC is the altitude between the two parallel sides AB and DC

So Area of trapezium will be given by

7) Find the area and perimeter of the right angle triangle whose hypotenuse is 5 cm and Base is

4cm

a)

b)

e)

d)

Solution (a)

By pythogrous theorem

Height

So Area

Perimeter

8) In an isosceles triangle AABC with AB = AC = 13 cm. D is mid-point on BC. Also BC = 10 cm which of the following is true?

a) Area of Triangle ABD and ADC are equal

b) Area of triangle ABD is

c) Area of triangle ABC is

d) All the above

Solution (d)

ABD an ADC are congruent triangle, So Area of Triangle ABD and ADC are equal

Also From pythogrous theorem, AD will be given as

AD

So Area of triangle ABC

9) A triangle and a parallelogram have the same base and the same area. The sides of the triangle are 26 cm and 30 cm and parallelogram stands on the base 28 cm. calculate the height of the parallelogram

a) 12 cm

b) 14 cm

c) 10 cm

d) 13 cm

Solution (a)

For triangle, all the sides are given, calculating the area using Heron formula

Now for parallelogram, Area is given by

Or H = 12 cm

10) Find the percentage increase in size of the triangle if each side is doubled

a) 200 %

b) 300 %

c) 400 %

d) None of the above

Solution (a)

**Match the column**

Perimeter of rectangle of length 24 cm and diagonal 26 cm | 22cm |

Perimeter of the square of side 10 cm | 17 cm |

Triangle of sides 4,5, 6 cm respectively | 40 cm |

Perimeter of parallelogram of two sides 5 and 6 cm respectively | 68 cm |