Q1. The formula for the area of a triangle is:
a) Base × Height
b) 2 × (Base × Height)
c) ½ × (Base × Height)
d) ½ × (Base + Height)
Answer: c
Q2. An equilateral triangle has a perimeter of 180 cm. Its area is:
a) 900 cm²
b) 900√3 cm²
c) 300√3 cm²
d) 600√3 cm²
Answer: b
Q3. A triangle with sides 122 m, 22 m, and 120 m has an area of:
a) 1320 m²
b) 1300 m²
c) 1400 m²
d) 1420 m²
Answer: a
Q4. A triangle has sides of 18 cm and 10 cm, with a perimeter of 42 cm. Its area is:
a) 20√11 cm²
b) 19√11 cm²
c) 22√11 cm²
d) 21√11 cm²
Answer: d
Q5. The sides of a triangle are in the ratio 12:17:25 and its perimeter is 540 cm. The area is:
a) 1000 cm²
b) 5000 cm²
c) 9000 cm²
d) 8000 cm²
Answer: c
Q6. An isosceles triangle has equal sides of 12 cm and its perimeter is 30 cm. The area is:
a) 9√15 cm²
b) 6√15 cm²
c) 3√15 cm²
d) √15 cm²
Answer: a
Q7. The area of an equilateral triangle with side √3/4 cm (using Heron’s formula) is:
a) 2/27 cm²
b) 2/15 cm²
c) 3√3/64 cm²
d) 3/14 cm²
Answer: c
Q8. The sides of a triangle are in the ratio 3:5:7 and its perimeter is 300 cm. Its area is:
a) 1000√3 cm²
b) 1500√3 cm²
c) 1700√3 cm²
d) 1900√3 cm²
Answer: b
Q9. In a right–angled triangle, the base is 8 cm and the hypotenuse is 10 cm. The area is:
a) 24 cm²
b) 40 cm²
c) 48 cm²
d) 80 cm²
Answer: a
Q10. A triangular board with sides 6 cm, 8 cm, and 10 cm is to be painted at 9 paise per cm². The cost is:
a) ₹2.00
b) ₹2.16
c) ₹2.48
d) ₹3.00
Answer: b
Q11. An isosceles right triangle has an area of 8 cm². Its hypotenuse is:
a) √32 cm
b) √16 cm
c) √48 cm
d) √24 cm
Answer: a
Q12. An isosceles triangle has a base of 2 cm and each equal side is 4 cm. Its area is:
a) √15 cm²
b) √(15/2) cm²
c) 2√15 cm²
d) 4√15 cm²
Answer: a
Q13. The perimeter of an equilateral triangle is 60 m. Its area is:
a) 10√3 m²
b) 15√3 m²
c) 20√3 m²
d) 100√3 m²
Answer: d
Q14. The sides of a triangle are 56 cm, 60 cm, and 52 cm. Its area is:
a) 1322 cm²
b) 1311 cm²
c) 1344 cm²
d) 1392 cm²
Answer: c
Q15. If the area of an equilateral triangle is 16√3 cm², then its perimeter is:
a) 48 cm
b) 24 cm
c) 12 cm
d) 36 cm
Answer: b
Q16. An equilateral triangle has an area of 9√3 cm². The length of its side is:
a) 8 cm
b) 36 cm
c) 4 cm
d) 6 cm
Answer: d
Q17. A triangle has sides 13 cm, 14 cm, and 15 cm. Its area (by Heron’s formula) is:
a) 84 cm²
b) 72 cm²
c) 91 cm²
d) 65 cm²
Answer: a
Q18. The semi–perimeter of a triangle with sides 7 cm, 24 cm, and 25 cm is:
a) 28 cm
b) 27 cm
c) 26 cm
d) 25 cm
Answer: a
Q19. A triangle has sides 15 cm, 20 cm, and 25 cm. Its area is:
a) 120 cm²
b) 150 cm²
c) 180 cm²
d) 200 cm²
Answer: b
Q20. Which of these correctly represents the area of a triangle using Heron’s formula?
a) √[s(s – a)(s – b)(s – c)]
b) √(abc)
c) ½ × base × height
d) a² + b² – c²
Answer: a
Q21. A triangle has sides 10 cm, 10 cm, and 12 cm. Its semi–perimeter is:
a) 14 cm
b) 15 cm
c) 16 cm
d) 17 cm
Answer: c
Q22. The area of an equilateral triangle with side length 12 cm is:
a) 36√3 cm²
b) 24√3 cm²
c) 48√3 cm²
d) 30√3 cm²
Answer: a
Q23. A triangle has sides 8 cm, 15 cm, and 17 cm. Identify its type and find its area.
a) Equilateral, 60 cm²
b) Right–angled, 60 cm²
c) Scalene, 64 cm²
d) Isosceles, 64 cm²
Answer: b
Q24. A triangle has sides 9 cm, 12 cm, and 15 cm. Its semi–perimeter is:
a) 18 cm
b) 17 cm
c) 16 cm
d) 15 cm
Answer: a
Q25. A triangle has sides 5 cm, 12 cm, and 13 cm. Its area is:
a) 24 cm²
b) 25 cm²
c) 26 cm²
d) 30 cm²
Answer: d
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