Basic Geometric Concepts - Exam Prep Problem Set

Basic Geometric Concepts - Problem Set

Q. If a circle has a radius of 5 cm, what is its area?

Solution

The area of a circle is given by the formula A = πr². Thus, A = π(5)² = 25π cm².

Correct Answer: A — 25π cm²

Q. What is the area of a triangle with a base of 4 units and a height of 3 units?

Solution

The area A of a triangle is given by A = 1/2 * base * height. Here, A = 1/2 * 4 * 3 = 6 square units.

Correct Answer: A — 6 square units

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

Solution

Using the Pythagorean theorem, c² = a² + b². Here, c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5 units.

Correct Answer: A — 5 units

Q. What is the length of the hypotenuse of a right triangle with legs of lengths 6 cm and 8 cm?

Solution

Using the Pythagorean theorem, c² = a² + b², where a = 6 cm and b = 8 cm. Thus, c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 cm.

Correct Answer: A — 10 cm

Q. What is the perimeter of a rectangle with length 5 units and width 3 units?

Solution

The perimeter P of a rectangle is given by P = 2(length + width). Here, P = 2(5 + 3) = 2(8) = 16 units.

Correct Answer: A — 15 units

Q. What is the perimeter of a triangle with sides measuring 6 cm, 8 cm, and 10 cm?

Solution

Perimeter = sum of all sides = 6 cm + 8 cm + 10 cm = 24 cm.

Correct Answer: A — 24 cm

Q. What is the volume of a cube with a side length of 2 units?

Solution

The volume V of a cube is given by V = side³. Here, V = 2³ = 8 cubic units.

Correct Answer: C — 8 cubic units

Q. Which of the following triangles is congruent to triangle ABC if AB = 5 cm, AC = 7 cm, and BC = 5 cm?

Solution

Triangles are congruent if they have the same side lengths. Triangle DEF has the same side lengths as triangle ABC.

Correct Answer: A — Triangle DEF with DE = 5 cm, DF = 7 cm, EF = 5 cm

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