Click on a question to see the answer and explanation.
▶1. What is the sum of the angles in any triangle?
Answer: 180°
Explanation:
- Step 1: The sum of the angles in any triangle is always the same.
- Step 2: This is a basic property of triangles.
▶2. A triangle has angles 50° and 60°. What is the third angle?
Answer: 70°
Explanation:
- Step 1: Sum of angles = 180°.
- Step 2: Third angle = 180° - (50° + 60°) = 70°.
▶3. If the sides of a triangle are 5 cm, 6 cm, and 7 cm, what is its perimeter?
Answer: 18 cm
Explanation:
- Step 1: Perimeter = sum of all sides.
- Step 2: Perimeter = 5 + 6 + 7 = 18 cm.
▶4. Find the area of a right-angled triangle with base 8 cm and height 6 cm.
Answer: 24 cm²
Explanation:
- Step 1: Area = (1/2) × base × height.
- Step 2: Area = (1/2) × 8 × 6 = 24 cm².
▶5. A triangle has sides 3 cm, 4 cm, and 5 cm. Is it a right-angled triangle?
Answer: Yes
Explanation:
- Step 1: Check if a² + b² = c² (Pythagoras Theorem).
- Step 2: 3² + 4² = 9 + 16 = 25; 5² = 25.
- Step 3: Since 9 + 16 = 25, it is a right-angled triangle.
▶6. What type of triangle has all sides equal?
Answer: Equilateral triangle
Explanation:
- Step 1: A triangle with all sides equal is called an equilateral triangle.
▶7. What is the area of an equilateral triangle with side 6 cm?
Answer: 9√3 cm²
Explanation:
- Step 1: Area = (√3/4) × side².
- Step 2: Area = (√3/4) × 6² = (√3/4) × 36 = 9√3 cm².
▶8. If two angles of a triangle are 40° and 70°, what is the third angle?
Answer: 70°
Explanation:
- Step 1: Sum of angles = 180°.
- Step 2: Third angle = 180° - (40° + 70°) = 70°.
▶9. A triangle has sides 7 cm, 24 cm, and 25 cm. Is it a right-angled triangle?
Answer: Yes
Explanation:
- Step 1: Check if a² + b² = c².
- Step 2: 7² + 24² = 49 + 576 = 625; 25² = 625.
- Step 3: Since 49 + 576 = 625, it is a right-angled triangle.
▶10. Find the perimeter of an equilateral triangle with side 9 cm.
Answer: 27 cm
Explanation:
- Step 1: Perimeter = 3 × side.
- Step 2: Perimeter = 3 × 9 = 27 cm.
▶11. If a triangle has sides 8 cm, 15 cm, and 17 cm, what is its area?
Answer: 60 cm²
Explanation:
- Step 1: Check if it is a right-angled triangle: 8² + 15² = 64 + 225 = 289; 17² = 289.
- Step 2: Since it is right-angled, area = (1/2) × base × height = (1/2) × 8 × 15 = 60 cm².
▶12. What is the name of a triangle with two equal sides?
Answer: Isosceles triangle
Explanation:
- Step 1: A triangle with two equal sides is called an isosceles triangle.
▶13. Find the area of a triangle with sides 7 cm, 8 cm, and 9 cm (use Heron's formula).
Answer: ≈ 26.83 cm²
Explanation:
- Step 1: s = (7 + 8 + 9)/2 = 12 cm.
- Step 2: Area = √[s(s-a)(s-b)(s-c)] = √[12 × 5 × 4 × 3] = √[720] ≈ 26.83 cm².
▶14. If all angles of a triangle are equal, what type of triangle is it?
Answer: Equilateral triangle
Explanation:
- Step 1: If all angles are equal, each angle is 60°.
- Step 2: Such a triangle is called an equilateral triangle.
▶15. A triangle has sides 10 cm, 10 cm, and 12 cm. What is its perimeter?
Answer: 32 cm
Explanation:
- Step 1: Perimeter = 10 + 10 + 12 = 32 cm.
▶16. What is the length of the altitude to the base of 10 cm in an equilateral triangle of side 10 cm?
Answer: 5√3 cm
Explanation:
- Step 1: Altitude = (√3/2) × side.
- Step 2: Altitude = (√3/2) × 10 = 5√3 cm.
▶17. If two triangles have all their corresponding angles equal, what can you say about them?
Answer: They are similar triangles
Explanation:
- Step 1: If all corresponding angles are equal, the triangles are similar.
▶18. A triangle has sides 13 cm, 14 cm, and 15 cm. Find its area (use Heron's formula).
Answer: ≈ 84 cm²
Explanation:
- Step 1: s = (13 + 14 + 15)/2 = 21 cm.
- Step 2: Area = √[21 × 8 × 7 × 6] = √[7056] ≈ 84 cm².
▶19. What is the sum of the exterior angles of any triangle?
Answer: 360°
Explanation:
- Step 1: The sum of the exterior angles of any polygon is 360°.
- Step 2: For a triangle, the sum is also 360°.
▶20. A ladder leans against a wall, making a triangle with the ground. If the ladder is 10 m long and the base is 6 m from the wall, how high does the ladder reach?
Answer: 8 m
Explanation:
- Step 1: This forms a right-angled triangle. Use Pythagoras Theorem: hypotenuse² = base² + height².
- Step 2: 10² = 6² + height² → 100 = 36 + height² → height² = 64 → height = 8 m.