Heron's Formula — Flashcards
Gujarat Board · Class 9 · Mathematics
20 flashcards for Heron's Formula (Gujarat Board Class 9 Mathematics) to test yourself on key terms and facts.
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What is Heron's Formula and who discovered it?
Answer
Heron's Formula (also called Hero's Formula) was discovered by Heron of Alexandria around 10 AD. It calculates the area of a triangle when all three sides are known, without needing to find the height…
State Heron's Formula for finding the area of a triangle.
Answer
Heron's Formula: Area = √[s(s-a)(s-b)(s-c)] where: • a, b, c are the three sides of the triangle • s is the semi-perimeter = (a+b+c)/2 • The result gives the area in square units…
What is semi-perimeter? How do you calculate it?
Answer
Semi-perimeter (s) is half of the perimeter of a triangle. Formula: s = (a+b+c)/2 where a, b, c are the three sides of the triangle. Example: If sides are 6 cm, 8 cm, 10 cm, then s = (6+8+10)/2 = 12 c…
When is Heron's Formula most useful?
Answer
Heron's Formula is most useful when: • All three sides of a triangle are known • The height of the triangle is difficult to calculate • You cannot easily identify a base and corresponding height • Wor…
Find the area of a triangle with sides 3 cm, 4 cm, and 5 cm using Heron's Formula.
Answer
Given: a = 3 cm, b = 4 cm, c = 5 cm Step 1: Calculate semi-perimeter s = (3+4+5)/2 = 6 cm Step 2: Apply Heron's Formula Area = √[s(s-a)(s-b)(s-c)] = √[6(6-3)(6-4)(6-5)] = √[6×3×2×1] = √36 = 6 cm²…
A triangular park has sides 40 m, 32 m, and 24 m. Find its area using Heron's Formula.
Answer
Given: a = 40 m, b = 32 m, c = 24 m Step 1: s = (40+32+24)/2 = 48 m Step 2: s-a = 48-40 = 8 m s-b = 48-32 = 16 m s-c = 48-24 = 24 m Step 3: Area = √[48×8×16×24] = √[147456] = 384 m² Note: This is a ri…
Find the area of an equilateral triangle with side 10 cm using Heron's Formula.
Answer
Given: All sides = 10 cm (a = b = c = 10) Step 1: s = (10+10+10)/2 = 15 cm Step 2: s-a = s-b = s-c = 15-10 = 5 cm Step 3: Area = √[15×5×5×5] = √[1875] = 25√3 cm² ≈ 25×1.732 = 43.3 cm²…
Two sides of a triangle are 8 cm and 11 cm, and the perimeter is 32 cm. Find the area.
Answer
Given: a = 8 cm, b = 11 cm, Perimeter = 32 cm Step 1: Find third side c = 32 - (8+11) = 13 cm Step 2: s = 32/2 = 16 cm Step 3: s-a = 8, s-b = 5, s-c = 3 Step 4: Area = √[16×8×5×3] = √[1920] = 8√30 cm²…
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