Area of a Trapezium and a Polygon
ICSE · Class 8 · Mathematics
Flashcards for Area of a Trapezium and a Polygon — ICSE Class 8 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Solve: Find the area of a triangle with base 12 cm and height 8 cm.
Answer
Step 1: Use area = (1/2) × base × height. Step 2: area = (1/2) × 12 × 8. Step 3: area = 6 × 8 = 48 cm². Answer: 48 cm²…
Solve: A triangle has sides 9 cm, 12 cm, and 15 cm. Find its area using Heron's formula.
Answer
Step 1: Find semi-perimeter. s = (9 + 12 + 15) / 2 = 36 / 2 = 18 cm. Step 2: Use Heron's formula. Area = √(s(s-a)(s-b)(s-c)) = √(18(18-9)(18-12)(18-15)) = √(18 × 9 × 6 × 3) = √2916 Step 3: Take square…
When do you use Heron's formula? Show a quick example.
Answer
Use Heron's formula when all three sides of a triangle are known and height is not given. Formula: Area = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2. Example: For sides 4 cm, 5 cm, 6 cm: s = (4+5+6)/2 =…
Solve: Find the area of an equilateral triangle whose side is 6 cm.
Answer
Step 1: Use area of equilateral triangle = (√3/4) a². Step 2: Put a = 6 cm. Area = (√3/4) × 6² = (√3/4) × 36 = 9√3 cm². Answer: 9√3 cm²…
Solve: A triangle has area 54 cm² and base 15 cm. Find its height.
Answer
Step 1: Use area = (1/2) × base × height. Step 2: 54 = (1/2) × 15 × h. Step 3: 54 = 7.5h. Step 4: h = 54 / 7.5 = 7.2 cm. Answer: 7.2 cm…
Solve: An isosceles triangle has base 12 cm and equal sides 10 cm each. Find its area.
Answer
Step 1: The perpendicular from the vertex to the base bisects the base. So, half of base = 12 / 2 = 6 cm. Step 2: Use Pythagoras in the right triangle. h² + 6² = 10² h² + 36 = 100 h² = 64 h = 8 cm. St…
What is the difference between base and height in a triangle?
Answer
Any side of a triangle can be taken as the base. The height is the perpendicular distance from the opposite vertex to that base. Base can be a slant side too, but height must always be perpendicular.
Solve: Find the perimeter of a triangle with sides 8 cm, 11 cm, and 13 cm.
Answer
Step 1: Perimeter of a triangle = sum of its three sides. Step 2: Perimeter = 8 + 11 + 13 = 32 cm. Answer: 32 cm…
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