Areas — Telangana (SSC) Class 9 Mathematics Solutions (Free)

Free step-by-step Telangana (SSC) Class 9 Mathematics solutions for "Areas" — important questions with detailed answers, download PDF for board exam preparation.

Areas — Telangana (SSC) Class 9 Mathematics Solutions (Free)

Free step-by-step Telangana (SSC) Class 9 Mathematics solutions for "Areas" — important questions with detailed answers, download PDF for board exam preparation.

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TL;DR: Free step-by-step Telangana (SSC) Class 9 Mathematics solutions for "Areas" — important questions with detailed answers, download PDF for board exam p…

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Areas — Textbook Questions Answered (8)

Q1: Find the area of a triangle with base 12 cm and height 8 cm.

Step 1: Area of triangle = (1/2) × base × height Step 2: Area = (1/2) × 12 × 8 Step 3: Area = (1/2) × 96 = 48 cm² Final Answer: Area = 48 cm²

Q2: Find the area of a parallelogram with base 10 cm and height 6 cm.

Step 1: Area of parallelogram = base × height Step 2: Area = 10 × 6 = 60 cm² Final Answer: Area = 60 cm²

Q3: Find the area of a trapezoid with parallel sides 8 cm and 12 cm, and height 5 cm.

Step 1: Area of trapezoid = (1/2) × (sum of parallel sides) × height Step 2: Area = (1/2) × (8 + 12) × 5 Step 3: Area = (1/2) × 20 × 5 = (1/2) × 100 = 50 cm² Final Answer: Area = 50 cm²

Q4: Find the area of a rhombus with diagonals 16 cm and 12 cm.

Step 1: Area of rhombus = (1/2) × d₁ × d₂ where d₁, d₂ are diagonals Step 2: Area = (1/2) × 16 × 12 Step 3: Area = (1/2) × 192 = 96 cm² Final Answer: Area = 96 cm²

Q5: Find the area of a circle with radius 7 cm.

Step 1: Area of circle = πr² Step 2: Area = π × 7² = 49π cm² Step 3: Area ≈ 49 × 3.14159 ≈ 153.94 cm² Final Answer: Area = 49π cm² ≈ 153.94 cm²

Q6: Prove that triangles on the same base and between the same parallels have equal area.

Step 1: Let triangles ABC and DBC share base BC and vertices A, D lie on a line parallel to BC Step 2: Let the perpendicular distance from A to BC = h Step 3: Let the perpendicular distance from D to BC = h (same, as they lie on parallel line) Step 4: Area of triangle ABC = (1/2) × BC × h Step 5: Area of triangle DBC = (1/2) × BC × h Step 6: Therefore, Area of ABC = Area of DBC Final Answer: Triangles on same base and between same parallels have equal area

Q7: Find the area of a triangle with sides 5 cm, 6 cm, and 7 cm using Heron's formula.

Step 1: a = 5, b = 6, c = 7 Step 2: Semi-perimeter s = (a + b + c)/2 = (5 + 6 + 7)/2 = 18/2 = 9 cm Step 3: Area = √[s(s-a)(s-b)(s-c)] Step 4: Area = √[9(9-5)(9-6)(9-7)] Step 5: Area = √[9 × 4 × 3 × 2] Step 6: Area = √[216] = √(36 × 6) = 6√6 cm² Step 7: Area ≈ 14.7 cm² Final Answer: Area = 6√6 cm² ≈ 14.7 cm²

Q8: Find the area of a sector of a circle with radius 10 cm and central angle 60°.

Step 1: Radius r = 10 cm, angle θ = 60° = π/3 radians Step 2: Area of sector = (θ/360°) × πr² (if angle in degrees) Step 3: Area = (60/360) × π × 10² Step 4: Area = (1/6) × π × 100 = (100π/6) = (50π/3) cm² Step 5: Area ≈ 52.36 cm² Final Answer: Area = (50π/3) cm² ≈ 52.36 cm²

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