Plane Geometry Practice Questions
ACT · ACT Math · 121 free MCQs with instant results and detailed explanations.
121
Total
38
Easy
62
Medium
21
Hard
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Sample Questions from Plane Geometry
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Q1
Easy
What is the area of a triangle with a base of 10 cm and a height of 5 cm?
A.
25 cm²
B.
30 cm²
C.
20 cm²
D.
50 cm²
Show Answer & Explanation
Correct Answer: A
The area of a triangle is calculated using the formula: Area = 1/2 * base * height. Therefore, Area = 1/2 * 10 cm * 5 cm = 25 cm².
Q2
Easy
What is the measure of each interior angle of a regular hexagon?
A.
120 degrees
B.
90 degrees
C.
108 degrees
D.
150 degrees
Show Answer & Explanation
Correct Answer: A
The formula for the interior angle of a regular polygon is (n-2) * 180° / n. For a hexagon (n=6), it is (6-2) * 180° / 6 = 120°.
Q3
Easy
What is the area of a rectangle with a length of 10 units and a width of 5 units?
A.
50 square units
B.
15 square units
C.
25 square units
D.
75 square units
Show Answer & Explanation
Correct Answer: A
The area of a rectangle is calculated by multiplying its length by its width. Here, 10 units * 5 units = 50 square units.
Q4
Medium
What is the area of a circle with a diameter of 14 cm?
A.
49π cm²
B.
14π cm²
C.
7π cm²
D.
98π cm²
Show Answer & Explanation
Correct Answer: A
The radius is half of the diameter, so radius = 7 cm. Area = πr² = π(7)² = 49π cm².
Q5
Medium
A right circular cone has a radius of 3 cm and a height of 4 cm. What is the volume of the cone?
A.
12π cm³
B.
9π cm³
C.
15π cm³
D.
6π cm³
Show Answer & Explanation
Correct Answer: A
The volume of a cone is calculated using the formula V = (1/3)πr²h. Substituting the values, V = (1/3)π(3²)(4) = 12π cm³.
Q6
Medium
In a right triangle, if one of the non-right angles measures 30 degrees and the hypotenuse is 8 cm, what is the length of the side opposite the 30-degree angle?
A.
4 cm
B.
6 cm
C.
8 cm
D.
2 cm
Show Answer & Explanation
Correct Answer: A
In a 30-60-90 triangle, the side opposite the 30-degree angle is half the hypotenuse. Thus, the length is 8 cm / 2 = 4 cm.
Q7
Medium
A rectangle has a length that is twice its width. If the perimeter is 48 cm, what is the width of the rectangle?
A.
8 cm
B.
12 cm
C.
10 cm
D.
6 cm
Show Answer & Explanation
Correct Answer: A
Let width be w, then length is 2w. The perimeter is given by P = 2(length + width), which gives 48 = 2(2w + w) => 48 = 6w => w = 8 cm.
Q8
Hard
A triangle has vertices at points A(2, 3), B(8, 3), and C(5, k). What value of k will make triangle ABC isosceles?
A.
1
B.
3
C.
5
D.
7
Show Answer & Explanation
Correct Answer: C
For triangle ABC to be isosceles, two sides must be equal. The lengths of AB and AC can be calculated. Setting them equal allows us to solve for k, leading to k = 5.
Q9
Hard
In a triangle, the lengths of the sides are in the ratio 3:4:5. If the perimeter of the triangle is 36 units, what is the length of the longest side?
A.
9 units
B.
12 units
C.
15 units
D.
18 units
Show Answer & Explanation
Correct Answer: C
The sides are in the ratio 3:4:5, meaning for every 3 + 4 + 5 = 12 parts, the longest side (5 parts) can be calculated. The total length of the sides is 36 units, thus each part is 36/12 = 3 units. The longest side is 5 parts which is 5 * 3 = 15 units.
Q10
Hard
In a triangle, the lengths of two sides are 10 cm and 15 cm. If the angle between them is 60 degrees, what is the area of the triangle?
A.
75 cm²
B.
100 cm²
C.
125 cm²
D.
150 cm²
Show Answer & Explanation
Correct Answer: A
The area of a triangle can be calculated using the formula: Area = (1/2) * a * b * sin(C), where a and b are the lengths of the sides and C is the included angle. Here, Area = (1/2) * 10 * 15 * sin(60°) = (1/2) * 10 * 15 * (√3/2) = 75 cm².
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Plane Geometry — ACT ACT Math Practice Questions Online
This page contains 121 practice MCQs for the chapter Plane Geometry in ACT ACT Math. The questions are organized by difficulty — 38 easy, 62 medium, 21 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.