Perimeters And Areas Of Plane Figures — Flashcards
NIOS · Class 10 · Maths
24 flashcards for Perimeters And Areas Of Plane Figures (NIOS Class 10 Maths) to test yourself on key terms and facts.
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Find the perimeter and area of a square of side 15 cm.
Answer
Step 1: Use square formulas. Perimeter = 4a and Area = a^2 Step 2: Substitute a = 15 cm. Perimeter = 4 × 15 = 60 cm Area = 15^2 = 225 cm² Answer: Perimeter = 60 cm, Area = 225 cm²…
Find the perimeter of a rectangle with length 50 m and breadth 40 m.
Answer
Step 1: Use the rectangle perimeter formula. Perimeter = 2(l + b) Step 2: Substitute l = 50 m and b = 40 m. Perimeter = 2(50 + 40) = 2 × 90 = 180 m Answer: 180 m…
Find the area of a parallelogram with base 12 cm and height 8 cm.
Answer
Step 1: Use the parallelogram area formula. Area = b × h Step 2: Substitute b = 12 cm and h = 8 cm. Area = 12 × 8 = 96 cm² Answer: 96 cm²…
A trapezium has parallel sides 30 cm and 20 cm and height 15 cm. Find its area.
Answer
Step 1: Use the trapezium area formula. Area = 1/2 × (a + b) × h Step 2: Substitute a = 30 cm, b = 20 cm, h = 15 cm. Area = 1/2 × (30 + 20) × 15 Area = 1/2 × 50 × 15 = 375 cm² Answer: 375 cm²…
Find the side and perimeter of a square whose diagonal is 30 cm.
Answer
Step 1: Use the diagonal formula for a square. Diagonal = a√2 Step 2: Solve for side. a = 30/√2 = 15√2 cm Step 3: Find perimeter. Perimeter = 4a = 4 × 15√2 = 60√2 cm Answer: Side = 15√2 cm, Perimeter …
A rectangle is 60 m long and 40 m wide. A path 4 m wide surrounds it outside. Find the area of the path.
Answer
Step 1: Find the outer dimensions. Outer length = 60 + 2 × 4 = 68 m Outer breadth = 40 + 2 × 4 = 48 m Step 2: Find outer area. Outer area = 68 × 48 = 3264 m² Step 3: Find inner area. Inner area = 60 ×…
Two cross paths of width 2.5 m run through the middle of a rectangle of length 50 m and breadth 25 m. Find the area of the paths.
Answer
Step 1: Use the cross-path formula. Area = w(l + b) - w² Step 2: Substitute w = 2.5 m, l = 50 m, b = 25 m. Area = 2.5(50 + 25) - (2.5)² Step 3: Simplify. Area = 2.5 × 75 - 6.25 = 187.5 - 6.25 = 181.25…
A triangle has sides 5 cm, 6 cm, and 7 cm. Find its area using Heron's Formula.
Answer
Step 1: Find the semi-perimeter. s = (a + b + c)/2 = (5 + 6 + 7)/2 = 18/2 = 9 cm Step 2: Apply Heron's Formula. Area = √(s(s-a)(s-b)(s-c)) Area = √(9(9-5)(9-6)(9-7)) Step 3: Simplify. Area = √(9 × 4 ×…
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