Practical Geometry

Q. If two triangles are similar, what can be said about their corresponding angles?

Solution

In similar triangles, corresponding angles are equal.

Correct Answer: A — They are equal

Q. What is the area of a circle with a diameter of 10 cm?

Solution

Area = π * (radius)² = π * (10/2)² = π * 25 = 25π cm².

Correct Answer: A — 25π cm²

Q. What is the area of a rectangle with a length of 8 cm and a width of 3 cm?

Solution

Area = length * width = 8 * 3 = 24 cm².

Correct Answer: A — 24 cm²

Q. What is the circumference of a circle with a radius of 7 cm?

Solution

Circumference = 2 * π * radius = 2 * π * 7 = 14π cm.

Correct Answer: A — 14π cm

Q. What is the distance between the points (3, 4) and (7, 1) in the coordinate plane?

Solution

Distance = √((7-3)² + (1-4)²) = √(4 + 9) = √13.

Correct Answer: A — 5 units

Q. What is the length of the hypotenuse of a right triangle with legs of 3 cm and 4 cm?

Solution

Using Pythagorean theorem: hypotenuse = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

Correct Answer: A — 5 cm

Q. What is the measure of each interior angle of a regular hexagon?

Solution

Each interior angle = (n-2) * 180° / n = (6-2) * 180° / 6 = 120°.

Correct Answer: A — 120°

Q. What is the perimeter of a square with a side length of 6 cm?

Solution

Perimeter = 4 * side = 4 * 6 = 24 cm.

Correct Answer: A — 24 cm

Q. What is the volume of a cylinder with a radius of 3 cm and a height of 5 cm?

Solution

Volume = π * radius² * height = π * 3² * 5 = 45π cm³.

Correct Answer: A — 45π cm³

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