Heron’s Formula Class 9 Worksheet Maths Chapter 10

Multiple Choice Questions

Q1: The difference between sides at right angles in a right angled triangle is 14 cm. The area of the triangle is 120 cm². The perimeter of the triangle is
(a) 80
(b) 45
(c) 60
(d) 64
Ans: (c)
Let y be one of the at right angle ,then another side will be y-14
Now we know that
A = (1/2)BH
120 = (1/2)y(y - 14)
y² - 14y - 240
(y - 24)(y + 10) = 0
y = 24
So other side is 10
From pythogrous theorem

So perimeter will be =10+24+26=60 cm

Q2: ABCD is a trapezium with AB  = 10cm, AD = 5 cm, BC = 4 cm and DC = 7 cm?
Find the area of the ABCD
(a) 34 cm²
(b) 28cm²
(c) 20 cm²
(d) None of these
Ans: (a)
BC is the altitude between the two parallel sides AB and DC
So Area of trapezium will be given by


Q3: Find the area and perimeter of the right angle triangle whose hypotenuse is 5 cm and Base is 4 cm
(a) 6 cm² ,12 cm
(b) 12 cm² ,14 cm
(c) 4 cm², 6 cm
(d) 12 cm² ,6 cm
Ans: (a)
By pythogorous theorem

So Area =(1/2) XBase X height = 6 cm²
Perimeter = 5 + 4 + 3 = 12 cm

Q4: In an isosceles triangle ?ABC 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 30 cm²
(c) Area of triangle ABC is 60 cm²
(d) All the above
Ans: (d)
ABD an ADC are congruent triangle, So Area of Triangle ABD and ADC are equal
Also From pythogorous theorem, AD will be given as

So Area of triangle ABC = (1/2)X base X height = 60 cm² 

Q5: 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) 10cm
(d) 13 cm
Ans: (a)
For triangle, all the sides are given, calculating the area using Heron formula
A = 336 cm²
Now for parallelogram, Area is given by
A = Base X Altitude
336 = 28 X H
Or H = 12 cm

True / False

Q1: Heron formula for area of triangle is not valid of all triangles
Ans: False

Q2: If each side of the triangles is tripled, the area will becomes 9 times.
Ans: True

Q3: Base and corresponding altitude of the parallelogram are 8 and 5 cm respectively. Area of parallelogram is 40 cm².
Ans: True

Q4: If each side of triangle is doubled, the perimeter will become 4 times.
Ans: False

Q5: If p is the perimeter of the triangle of sides a,b,c ,the area of triangle is.

Ans: True

Q6: When two triangles are congruent, there areas are same.
Ans: True

Q7: Heron’s belongs to America.
Ans: False

Q8:  If the side of the equilateral triangle is a rational number, the area would always be irrational number.
Ans: True

Concepts Questions

Q1: Triangle have sides as a=5 cm ,b=4 cm,c=3 cm
Ans: 
Area

Q2: Equilateral triangle having side a=2 cm
Ans: Area of equilateral


Q3: Right angle triangle have base=4 cm and Height =3 cm
Ans: Area of triangle
A = (1/2)BH = 6cm²

Q4: Square whose diagonal is 10 cm
Ans: Area of square in terms diagonal
A = (1/2)d² = 50cm²

Q5: Rectangle whose length and breath are 6 and 4 cm
Ans: Rectangle area is given by
A = LXB = 24cm²

Q6: Parallelogram whose two sides are 10 cm and 16 cm and diagonal is 14 cm
Ans: In parallelogram whose two sides and diagonal are given, Area is given by

Where
So s=20cm
So A=80(3)^1/2cm² 

Q7: Parallelogram whose base is 10 cm and height is 14 cm
Ans: Area is given by
A = Base X height = 10X14 = 140cm²

Q8: Rhombus of diagonals to 10 and 24 cm
Ans: Area is given by
A=(1/2)d₁d₂ = 120cm²

Q9: Two sides of trapezium are 36 and 24 cm and its altitude is
Ans: Area of trapezium is given by
A = (1/2)(Sum of parallel sides) Altitude
A = 360cm²