Practice Questions
Concept Explanation
A triangle has three sides and three angles. Types include equilateral (all sides equal), isosceles (two sides equal), scalene (no sides equal), and right-angled (one 90° angle).
Key Formulas
- Area = ½ × base × height (sq units)
- Heron’s formula: Area = √(s(s − a)(s − b)(s − c)), where s = (a + b + c)/2
- Pythagoras theorem (right triangle): a² + b² = c², where c is the hypotenuse
- Angle sum = 180°
Example
Right triangle with legs 3 cm and 4 cm: hypotenuse = √(9 + 16) = 5 cm. Area = ½ × 3 × 4 = 6 sq cm.
Common Trap
In Heron’s formula, use semi-perimeter s, not full perimeter.
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Q1 Easy
Area of a triangle with base 10 cm and height 6 cm is:
ExplanationArea = ½ × 10 × 6 = 30 sq cm. -
Q2 Easy
In a right triangle, legs are 3 cm and 4 cm. The hypotenuse is:
Explanationc = √(3² + 4²) = √25 = 5 cm. -
Q3 Easy
Sides of a triangle are 3 cm, 4 cm and 5 cm. Using Heron’s formula, area is:
Explanations = 6. Area = √(6 × 3 × 2 × 1) = 6 sq cm. -
Q4 Easy
In a right triangle, hypotenuse is 13 cm and one leg is 5 cm. The other leg is:
ExplanationOther leg = √(13² − 5²) = √144 = 12 cm. -
Q5 Medium
An equilateral triangle has side 6 cm. Its height is:
ExplanationHeight = (√3/2) × 6 = 3√3 cm. -
Q6 Medium
An isosceles triangle has equal sides 5 cm and base 6 cm. Its area is:
ExplanationHeight from base = √(5² − 3²) = 4 cm. Area = ½ × 6 × 4 = 12 sq cm. -
Q7 Easy
Perimeter of a triangle with sides 7 cm, 8 cm and 9 cm is:
ExplanationPerimeter = 7 + 8 + 9 = 24 cm.
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Q8 Medium
A right triangle has legs 8 cm and 15 cm. The hypotenuse is:
Explanationc = √(64 + 225) = √289 = 17 cm. -
Q9 Easy
Area of a triangle with base 14 cm and height 5 cm is:
ExplanationArea = ½ × 14 × 5 = 35 sq cm. -
Q10 Hard
Sides 13 cm, 14 cm and 15 cm form a triangle. Its area (Heron) is:
Explanations = 21. Area = √(21 × 8 × 7 × 6) = 84 sq cm. -
Q11 Medium
In a 30°-60°-90° triangle, the side opposite 30° is 5 cm. The hypotenuse is:
ExplanationSide opposite 30° is half the hypotenuse, so hypotenuse = 10 cm. -
Q12 Medium
A triangle has angles in ratio 1 : 2 : 3. It is a:
ExplanationAngles: 30°, 60°, 90° — a right triangle. -
Q13 Hard
Equilateral triangle side 10 cm. Area is:
ExplanationArea = (√3/4) × 10² = 25√3 sq cm. -
Q14 Hard
Base of a triangle is doubled and height halved. The area:
ExplanationArea = ½bh. New area = ½(2b)(h/2) = ½bh — unchanged.
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DS1 Easy
What is the area of the right triangle?
Statement IThe legs are 6 cm and 8 cm.
Statement IIThe hypotenuse is 10 cm.
ExplanationStatement I alone: area = ½ × 6 × 8 = 24 sq cm. Statement II alone does not fix the legs. -
DS2 Easy
What is the hypotenuse of a right triangle?
Statement IOne leg is 9 cm.
Statement IIThe other leg is 12 cm.
ExplanationNeed both legs: hypotenuse = √(81 + 144) = 15 cm.
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DS3 Easy
What is the area of the triangle?
Statement IBase is 12 cm.
Statement IIHeight is 7 cm.
ExplanationNeed both: area = ½ × 12 × 7 = 42 sq cm. -
DS4 Medium
What is the third side of a triangle with sides 5 cm and 12 cm?
Statement IIt is a right triangle.
Statement IIThe third side is the hypotenuse.
ExplanationNeed both to conclude the third side is √(25 + 144) = 13 cm.