PARCC Geometry Practice Questions 2 — Questions and Answers

Question 1: What is the area of a triangle with a base of 10 cm and a height of 6 cm?

60 cm²
30 cm² (Correct answer)
16 cm²
20 cm²

Correct answer: 30 cm²

Area of a triangle = (1/2) × base × height = (1/2) × 10 × 6 = 30 cm².

The area of a triangle is calculated using the formula: A = (1/2) × b × h where b is the length of the base and h is the perpendicular height (altitude). For this triangle: A = (1/2) × 10 cm × 6 cm A = (1/2) × 60 cm² A = 30 cm² The formula A = (1/2)bh comes from the fact that a triangle is exactly half of a parallelogram with the same base and height. If you draw a diagonal across a rectangle or parallelogram, you get two congruent triangles, each with half the area. Important note: the height must be perpendicular to the base. In a right triangle, the two legs serve as base and height. In an obtuse triangle, the height may fall outside the triangle. The PARCC exam may present triangles in various orientations; always identify the perpendicular height correctly.

Question 2: A circle has a radius of 5 inches. What is its circumference? (Use π ≈ 3.14)

15.7 in
31.4 in (Correct answer)
78.5 in
25 in

Correct answer: 31.4 in

Circumference = 2πr = 2 × 3.14 × 5 = 31.4 inches.

The circumference of a circle (the distance around its edge) is calculated using the formula: C = 2πr or equivalently C = πd where r is the radius and d is the diameter (d = 2r). For a circle with radius 5 inches: C = 2 × π × 5 C = 2 × 3.14 × 5 C = 6.28 × 5 C = 31.4 inches The area of this circle would be: A = πr² = 3.14 × 5² = 3.14 × 25 = 78.5 in². Notice that 78.5 is one of the answer choices—this is a common distractor because students sometimes confuse the area and circumference formulas. Remember: - Circumference uses the radius (or diameter): C = 2πr or C = πd → result has units like inches, cm - Area uses the radius squared: A = πr² → result has square units like in², cm² The PARCC exam frequently includes problems with both area and circumference to test whether students use the correct formula.

Question 3: Two angles of a triangle measure 45° and 75°. What is the measure of the third angle?

40°
60° (Correct answer)
80°
120°

Correct answer: 60°

The sum of angles in a triangle is 180°. Third angle = 180° − 45° − 75° = 60°.

The Triangle Angle Sum Theorem states that the interior angles of any triangle always sum to exactly 180°. This is a fundamental theorem of Euclidean geometry. To find the unknown angle: Angle₁ + Angle₂ + Angle₃ = 180° 45° + 75° + Angle₃ = 180° 120° + Angle₃ = 180° Angle₃ = 180° − 120° = 60° We can verify: 45° + 75° + 60° = 180° ✓ This triangle has angles of 45°, 75°, and 60°—all are acute (less than 90°), so this is an acute triangle. The Triangle Angle Sum Theorem is used to: - Find unknown angles in triangles - Classify triangles (acute: all angles < 90°; right: one angle = 90°; obtuse: one angle > 90°) - Solve geometry problems involving parallel lines cut by transversals This is one of the most frequently tested geometry concepts on the PARCC exam.

Question 4: What is the volume of a rectangular prism with length 8 cm, width 5 cm, and height 3 cm?

40 cm³
79 cm³
120 cm³ (Correct answer)
240 cm³

Correct answer: 120 cm³

Volume = length × width × height = 8 × 5 × 3 = 120 cm³.

The volume of a rectangular prism (a box shape) is found by multiplying its three dimensions: V = l × w × h For this prism: V = 8 cm × 5 cm × 3 cm V = 40 cm² × 3 cm (area of base times height) V = 120 cm³ Note that volume is measured in cubic units (cm³, m³, ft³, etc.) because you are multiplying three lengths together. The formula V = lwh can also be thought of as V = (Area of base) × height. The area of the rectangular base is 8 × 5 = 40 cm², and multiplying by the height 3 cm gives 120 cm³. This interpretation—base area times height—generalizes to ALL prisms: V = Bh, where B is the area of the base and h is the height. So a triangular prism would have V = (1/2 × b × h_triangle) × H_prism. Understanding this general formula helps on PARCC problems involving various 3D shapes.

Question 5: Which of the following statements is true about the sum of exterior angles of any convex polygon?

It equals 180°.
It equals 360°. (Correct answer)
It equals the number of sides × 90°.
It depends on the number of sides.

Correct answer: It equals 360°.

The sum of the exterior angles of any convex polygon, one at each vertex, always equals 360°, regardless of the number of sides.

The Exterior Angle Sum Theorem states that the sum of the exterior angles of any convex polygon (one exterior angle per vertex) is always 360°, regardless of the number of sides or the type of polygon. Intuitive proof: Imagine walking along the perimeter of a convex polygon. At each vertex, you turn through an exterior angle. When you complete the walk and return to your starting point facing the original direction, you have made exactly one complete turn = 360°. Examples: - Triangle: exterior angles sum to 360° (each exterior angle ≈ 120° for equilateral triangle; 3 × 120° = 360°) - Square: each exterior angle = 90°; 4 × 90° = 360° - Regular hexagon: each exterior angle = 60°; 6 × 60° = 360° Note: the sum of INTERIOR angles does depend on the number of sides: sum = (n − 2) × 180°, where n is the number of sides. But exterior angles always sum to 360°. Confusing interior and exterior angle sums is a common error on the PARCC exam geometry section.

Question 6: A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

10 (Correct answer)
12
14
√100

Correct answer: 10

By the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100. So c = √100 = 10.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides (the legs): a² + b² = c² For legs a = 6 and b = 8: c² = 6² + 8² c² = 36 + 64 c² = 100 c = √100 = 10 The hypotenuse is 10 units long. This is a famous Pythagorean triple: (6, 8, 10), which is just a scaled-up version of the (3, 4, 5) triple (multiply each by 2). Note: √100 = 10 and 10 are the same value, so answer choices A (10) and D (√100) are actually equivalent. The question intends 10 as the final simplified form. Knowing the common Pythagorean triples saves time on standardized tests: - (3, 4, 5) and multiples: (6, 8, 10), (9, 12, 15)... - (5, 12, 13) and multiples - (8, 15, 17) - (7, 24, 25)

PARCC Geometry Practice Questions 2

What is the area of a triangle with a base of 10 cm and a height of 6 cm?