Geometry Practice Questions
Common Core (US) · Common Core Math Grade 6 · 125 free MCQs with instant results and detailed explanations.
125
Total
47
Easy
58
Medium
20
Hard
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Sample Questions from Geometry
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Q1
Easy
What is the area of a rectangle with a length of 8 units and a width of 3 units?
A.
24 square units
B.
11 square units
C.
32 square units
D.
20 square units
Show Answer & Explanation
Correct Answer: A
The area of a rectangle is calculated by multiplying the length by the width. Here, Area = Length × Width = 8 × 3 = 24 square units.
Q2
Easy
Which shape has exactly 4 equal sides and 4 right angles?
A.
Rectangle
B.
Rhombus
C.
Square
D.
Trapezoid
Show Answer & Explanation
Correct Answer: C
A square is defined as a shape with four equal sides and four right angles. This distinguishes it from other quadrilaterals.
Q3
Easy
If a triangle has a base of 10 cm and a height of 5 cm, what is its area?
A.
25 square cm
B.
50 square cm
C.
15 square cm
D.
30 square cm
Show Answer & Explanation
Correct Answer: A
The area of a triangle is calculated using the formula: Area = 1/2 × Base × Height. Here, Area = 1/2 × 10 × 5 = 25 square cm.
Q4
Medium
A rectangle has a length that is twice its width. If the perimeter of the rectangle is 36 cm, what is the length of the rectangle?
A.
12 cm
B.
18 cm
C.
24 cm
D.
9 cm
Show Answer & Explanation
Correct Answer: A
Let the width be w. Then the length is 2w. The perimeter P = 2(length + width) = 2(2w + w) = 6w. Setting this equal to 36 cm, we get 6w = 36, so w = 6 cm and length = 12 cm.
Q5
Medium
If the radius of a circle is increased by 50%, what will be the percentage increase in the area of the circle?
A.
125%
B.
50%
C.
75%
D.
100%
Show Answer & Explanation
Correct Answer: A
When the radius increases by 50%, the new radius is 1.5r. The area increases from πr² to π(1.5r)² = π(2.25r²), which is a 125% increase (from original area).
Q6
Medium
What is the volume of a rectangular prism with a length of 8 cm, width of 4 cm, and height of 3 cm?
A.
96 cm³
B.
60 cm³
C.
32 cm³
D.
24 cm³
Show Answer & Explanation
Correct Answer: A
The volume of a rectangular prism is calculated by multiplying length, width, and height. Volume = length * width * height = 8 * 4 * 3 = 96 cm³.
Q7
Medium
Which of the following shapes has exactly four right angles?
A.
Parallelogram
B.
Trapezoid
C.
Rectangle
D.
Rhombus
Show Answer & Explanation
Correct Answer: C
A rectangle is defined as a quadrilateral with four right angles. While other shapes may have right angles, only rectangles consistently have all four right angles.
Q8
Hard
A rectangular prism has a length of 15 cm, a width of 10 cm, and a height of 5 cm. What is the total surface area of the prism?
A.
350 cm²
B.
600 cm²
C.
400 cm²
D.
500 cm²
Show Answer & Explanation
Correct Answer: B
The total surface area (SA) of a rectangular prism is calculated using the formula SA = 2lw + 2lh + 2wh. Here, l = 15 cm, w = 10 cm, and h = 5 cm. Thus, SA = 2(15*10) + 2(15*5) + 2(10*5) = 300 + 150 + 100 = 600 cm².
Q9
Hard
A rectangular prism has a length of 10 cm, a width of 4 cm, and a height of 6 cm. If the prism is cut in half parallel to its length, what is the volume of one half of the prism?
A.
120 cm³
B.
60 cm³
C.
240 cm³
D.
80 cm³
Show Answer & Explanation
Correct Answer: A
The volume of the original prism is found by multiplying length, width, and height: 10 cm * 4 cm * 6 cm = 240 cm³. Cutting it in half gives 240 cm³ / 2 = 120 cm³ for one half.
Q10
Hard
A triangle has two sides measuring 8 cm and 15 cm. If the angle between these two sides is 60 degrees, what is the length of the third side using the Law of Cosines?
A.
10 cm
B.
12 cm
C.
14 cm
D.
18 cm
Show Answer & Explanation
Correct Answer: C
Using the Law of Cosines: c² = a² + b² - 2ab * cos(C) with a = 8 cm, b = 15 cm, and C = 60 degrees. The calculation yields c = 14 cm.
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Geometry — Common Core (US) Common Core Math Grade 6 Practice Questions Online
This page contains 125 practice MCQs for the chapter Geometry in Common Core (US) Common Core Math Grade 6. The questions are organized by difficulty — 47 easy, 58 medium, 20 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.