[CLASS 9] Mathematics MCQs on Heron’s Formula & Area of a Triangle by Heron’s Formula

Mathematics Multiple Choice Questions on “Heron’s Formula & Area of a Triangle by Heron’s Formula”.

1. Which of the following formula is used for finding the area of triangle?
a) base * height
b) (frac{1}{2}) * base * height
c) 2 * base * height
d) base² * height
Answer: b

2. In heron’s formula (sqrt{s*(s-a)*(s-b)*(s-c)}), what is the value of s if a, b and c are sides of the triangle?
a) (frac{a+b+c}{4})
b) a+b+c
c) (frac{a+b+c}{2})
d) 2a+2b+2c

Answer: c
Clarification: In heron’s formula (sqrt{s*(s-a)*(s-b)*(s-c)}), s is the half perimeter of the triangle.
Perimeter of the triangle having sides a, b and c is a + b + c.
Hence, s = half perimeter of the triangle = (frac{a+b+c}{2}).

3. What is the area of the triangle having sides equal to 10 cm, 16 cm and 24 cm?
a) (25sqrt{15} cm^2)
b) (35sqrt{17} cm^2)
c) (15sqrt{13} cm^2)
d) (15sqrt{15} cm^2)

Answer: d
Clarification: a = 10, b = 16 and c = 24
s = (frac{a+b+c}{2}=frac{10+16+24}{2} = frac{50}{2}) = 25
According to heron’s formula, area of the triangle = (sqrt{s*(s-a)*(s-b)*(s-c)})
= (sqrt{25*(25-10)*(25-16)*(25-24)})
= (sqrt{25*15*9*1})
= (15sqrt{15} cm^2)

4. The sides of a triangle are in the proportion of 2 : 3 : 5 and its perimeter is 200 cm. The area of this triangle is __________ cm².
a) 375 (sqrt{23})
b) 375 (sqrt{21})
c) 345 (sqrt{23})
d) 345 (sqrt{21})

Answer: a
Clarification: Let the side of a triangles be a = 2x, b = 3x and c = 5x.
Perimeter of the triangle is 200 cm.
Therefore a + b + c = 2x + 3x + 5x = 200
10x = 200
Hence, x = 20
a = 2x = 2(20) = 40 cm
b = 3x = 3(30) = 90 cm
c = 5x = 5(20) = 100 cm
Now, s = (frac{a+b+c}{2}=frac{40+90+100}{2} = frac{230}{2}) = 115
According to heron’s formula, area of the triangle = (sqrt{s*(s-a)*(s-b)*(s-c)})
= (sqrt{115*(115-40)*(115-90)*(115-100)})
= (sqrt{115*75*25*15})
= (375 sqrt{23})

5. A triangular board having sides 45m, 30m and 35m is used for advertising. One company uses this board for its advertisement for 4 months. How much rent will the company has to pay if the rent is Rs 3500 per m²?
a) Rs 611800
b) Rs 1835400
c) Rs 611900
d) Rs 1835500

Answer: a
Clarification: a = 45, b = 30 and c = 35
We know that s = (frac{a+b+c}{2} = frac{45+30+35}{2} = frac{110}{2}) = 55
According to heron’s formula, area of the triangle = (sqrt{s*(s-a)*(s-b)*(s-c)})
= (sqrt{55*(55-45)*(55-30)*(55-35)})
= (sqrt{55*10*25*20})
= 524.40 m²
Now the rent for 1 m² = Rs 3500,
then rent for 992.15 m² = 524.40 * 3500 = Rs 18,35,400
The rent which we got above is for one year.
The company used the board for 4 months.
Therefore rent for 4 months = Rs (frac{18,35,400*4}{12})
= Rs 6,11,800.