Mathematical Reasoning Geometry and Measurement 1 Flashcards

A circular garden has a radius of 7 meters. What is the area of the garden? (Use π ≈ 3.14)

Answer: 153.86 square meters

The area of a circle is A = πr². With r = 7, A = 3.14 × 7² = 3.14 × 49 = 153.86 square meters.

What is the perimeter of a square with a side length of 9 inches?

Answer: 36 inches

A square has 4 equal sides, so its perimeter is 4 × side = 4 × 9 = 36 inches.

A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume? (Use π ≈ 3.14)

Answer: 282.6 cubic cm

The volume of a cylinder is V = πr²h = 3.14 × 3² × 10 = 3.14 × 9 × 10 = 282.6 cubic cm.

A trapezoid has parallel sides of 8 ft and 12 ft, and a height of 5 ft. What is its area?

Answer: 100 square feet

Area of a trapezoid = ½ × (base₁ + base₂) × height = ½ × (8 + 12) × 5 = ½ × 20 × 5 = 50. Wait — ½ × 20 × 5 = 50, but let me recalculate: ½ × (8+12) × 5 = 0.5 × 20 × 5 = 50. The correct answer is 50 square feet.

How many degrees are in the sum of the interior angles of a triangle?

Answer: 180 degrees

The interior angles of any triangle always add up to 180 degrees, a fundamental property of triangles.

A rectangular swimming pool is 25 meters long and 10 meters wide. If you want to put a fence around the entire pool, how many meters of fencing do you need?

Answer: 70 meters

The perimeter of a rectangle is P = 2 × (length + width) = 2 × (25 + 10) = 2 × 35 = 70 meters.