Geometric Shapes and Mensuration Flashcards

A rectangular garden is 25 m long and 15 m wide. If fencing costs $3 per meter, what is the total cost to enclose the garden?

Answer: $240

Perimeter = 2(25 + 15) = 80 m; total cost = 80 × $3 = $240.

What is the diagonal length of a rectangle with length 12 cm and width 5 cm?

Answer: 13 cm

Diagonal = √(12² + 5²) = √(144 + 25) = √169 = 13 cm.

How many cubes of side 2 cm can fit exactly inside a box measuring 8 cm × 6 cm × 4 cm?

Answer: 24

Box volume = 192 cm³; small cube volume = 2³ = 8 cm³; number of cubes = 192 ÷ 8 = 24.

A circle is inscribed in a square with side 14 cm. What is the area of the region between the square and the circle? (Use π = 22/7)

Answer: 42 cm²

Square area = 196 cm²; circle area = πr² = (22/7) × 7² = 154 cm²; difference = 196 − 154 = 42 cm².

The perimeter of an equilateral triangle is 36 cm. What is its area? (Use √3 ≈ 1.73)

Answer: 62.3 cm²

Side = 36 ÷ 3 = 12 cm; Area = (√3/4) × 12² = (1.73/4) × 144 ≈ 62.3 cm².

A path 1 m wide is built around a rectangular garden measuring 20 m × 10 m. What is the area of the path alone?

Answer: 64 m²

Outer rectangle = 22 × 12 = 264 m²; inner garden = 200 m²; path area = 264 − 200 = 64 m².

A cylindrical water tank has radius 3.5 m and height 10 m. What is its capacity in liters? (Use π = 22/7; 1 m³ = 1,000 L)

Answer: 385,000 L

Volume = πr²h = (22/7) × 12.25 × 10 = 385 m³; capacity = 385 × 1,000 = 385,000 L.