Mensuration
Tamil Nadu Board · Class 9 · Mathematics
Flashcards for Mensuration — Tamil Nadu Board Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Find the area of a triangle with sides 13 cm, 14 cm, and 15 cm using Heron's formula.
Answer
Step 1: Calculate semi-perimeter s = (a+b+c)/2 = (13+14+15)/2 = 42/2 = 21 cm Step 2: Apply Heron's formula: Area = √[s(s-a)(s-b)(s-c)] Step 3: Area = √[21(21-13)(21-14)(21-15)] Step 4: Area = √[21 × 8…
Formula for area of a triangle using Heron's formula
Answer
Formula: Area = √[s(s-a)(s-b)(s-c)] sq. units Where: s = (a+b+c)/2 (semi-perimeter) a, b, c = the three sides of the triangle Example: Triangle with sides 10 cm, 24 cm, 26 cm s = (10+24+26)/2 = 30 cm…
A triangular field has sides 28 m, 15 m, and 41 m. Find the area and cost of levelling at ₹20 per m².
Answer
Step 1: Calculate s = (28+15+41)/2 = 84/2 = 42 m Step 2: Apply Heron's formula Area = √[42(42-28)(42-15)(42-41)] Area = √[42 × 14 × 27 × 1] Area = √[15876] = √[2×3×7 × 7×2 × 3³] = 2×3×7×3 = 126 m² Ste…
Three triangular plots have the same perimeter of 120 m with sides: (i) 30, 40, 50 m (ii) 35, 40, 45 m (iii) 40, 40, 40 m. Which plot is most spacious?
Answer
Plot (i) - Right angled triangle: s = 60 m Area = √[60×30×20×10] = √[360000] = 600 m² Plot (ii) - Acute angled triangle: s = 60 m Area = √[60×25×20×15] = √[450000] = 300√5 ≈ 670.8 m² Plot (iii) - Eq…
Find the area of a quadrilateral ABCD with sides AB=13 cm, BC=12 cm, CD=9 cm, AD=14 cm and diagonal BD=15 cm.
Answer
Method: Divide into two triangles using diagonal BD Triangle ABD: sides 13 cm, 14 cm, 15 cm s = (13+14+15)/2 = 21 cm Area = √[21×8×7×6] = √[7056] = 84 cm² Triangle BCD: sides 12 cm, 9 cm, 15 cm s = …
A rhombus has perimeter 400 m and one diagonal 120 m. Find its area using Heron's formula.
Answer
Step 1: Find each side of rhombus Perimeter = 4 × side = 400 m Side = 100 m Step 2: In triangle ABC formed by two sides and diagonal Sides of triangle: a=100 m, b=100 m, c=120 m (diagonal) s = (100+1…
Find the Total Surface Area (TSA) of a cuboid with length 7.5 m, breadth 3 m, and height 5 m.
Answer
Formula: TSA = 2(lb + bh + lh) sq. units Given: l = 7.5 m, b = 3 m, h = 5 m Step 1: Calculate each product lb = 7.5 × 3 = 22.5 m² bh = 3 × 5 = 15 m² lh = 7.5 × 5 = 37.5 m² Step 2: Sum the products …
Find the Lateral Surface Area (LSA) of a cuboid with length 7.5 m, breadth 3 m, and height 5 m.
Answer
Formula: LSA = 2(l + b)h sq. units (LSA excludes top and bottom faces) Given: l = 7.5 m, b = 3 m, h = 5 m Step 1: Add length and breadth l + b = 7.5 + 3 = 10.5 m Step 2: Multiply by 2 and height LS…
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