Class 9 Area of a Triangle by Heron's Formula — practice questions with answers
Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. In Heron's formula, what does the letter s usually stand for?
AThe semi-perimeter of the triangle
BThe shortest side of the triangle
CThe full perimeter of the triangle
DThe area of the triangle
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Answer: A) The semi-perimeter of the triangle
Heron's formula uses s=2a+b+c, the semi-perimeter (half of the perimeter).
2. The sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 36 cm. What are the sides?
A9 cm, 12 cm, 15 cm
B6 cm, 8 cm, 10 cm
C12 cm, 16 cm, 20 cm
D3 cm, 4 cm, 5 cm
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Answer: A) 9 cm, 12 cm, 15 cm
Let sides be 3x, 4x, 5x. Then 12x = 36 => x = 3. Sides are 9, 12, 15 cm.
3. A triangular park in Pune has sides 50 m, 78 m and 112 m. The municipal gardener needs the area to plan grass turf. Using Heron's formula, find the area of the park (in m²).
A1680
B1850
C3360
D1510
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Answer: A) 1680
s=250+78+112=120. Area = 120⋅(120−50)⋅(120−78)⋅(120−112)=120⋅70⋅42⋅8=2822400=1680 m².
4. A triangular piece of land has sides 41 m, 28 m and 15 m. The owner wishes to plant trees along the longest altitude (the altitude drawn to the longest side). First find the area (in m²).
A141
B252
C126
D111
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Answer: C) 126
s=241+28+15=42. Area = 42⋅(42−41)⋅(42−28)⋅(42−15)=42⋅1⋅14⋅27=15876=126 m².
5. A triangular plot has sides 35 m, 54 m and 61 m. It is to be levelled at Rs 4 per square metre. If the total bill is to be estimated, find the area (in m²) first.
A939.15
B1878.3
C844.15
D1034.15
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Answer: A) 939.15
s=235+54+61=75. Area = 75⋅(75−35)⋅(75−54)⋅(75−61)=75⋅40⋅21⋅14=882000=939.15 m² (rounded to 2 decimals).