Geometry Questions and Answers

March 7, 2024

Geometry Questions and Answers

In this page we will recap through some basic information related to Geometry and then we will be solving Geometry Questions and Answers which will help you in tackling questions if asked in the exams.

Definition In its simplest form, geometry is the mathematical study of shapes and space. Geometry can deal with flat, two-dimensional shapes, such as squares and circles, or three-dimensional shapes with depth, such as cubes and spheres.

Concept

Before diving into two-dimensional and three-dimensional shapes, consider the basic geometric objects that create these shapes: points, lines, line segments, rays, and planes.

A point is represented by a dot and shows a location in space.
A line is a set of straight points that extends forever in both directions as depicted by arrows on both ends.
Rays are lines that end on one side. Line segments end on both sides. Planes are surfaces that extend forever in all directions.

There are two types of shapes where the concept of geometry revolves, those are 3D and 2D shapes. Let us know them about in brief:

Two-dimensional objects only have two dimensions: length and width.
Unlike two-dimensional objects, three-dimensional objects have a third dimension, depth, and are, therefore, not flat. Cubes, spheres, and pyramids are examples of three-dimensional objects. A cube is an object made of six square sides.

Sample Geometry Questions and Answers are given below:

1. If angles P and Q are complementary to one another, and angle P is two times of angle Q. Calculate the measures of angles P and Q.

60°

51.34%

90°

29.41%

120°

10.16%

None

9.09%

Let the measure of angle P be P, and the measure of angle Q be Q.

P = 2Q

Given that angles P and Q are complementary. Therefore,

P + Q = 90⁰

But, P = 2Q. Therefore,

2Q + Q = 90

3Q = 90

Q= 90/3 = 30⁰

P =2Q = 60^°

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2. What is the value of angle A in the given figure?

30°

6.25%

70°

85.42%

80°

3.13%

90°

5.21%

To calculate the measure of angle A, we have to calculate the value of angle B.

Angle B = 180-130= 50⁰

Therefore, the measure of angle A = 180 – (50+60)

A = 180-110

A =70^°

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3. The given triangle ABC is a right triangle. Angle ABC is 60⁰. Find the measure of triangle APC.

56°

4.52%

40°

9.68%

75°

76.13%

80°

9.68%

The sum of all the angles in the given triangle ABC is 180⁰

180 = 60 + 90 + BCA

Therefore, angle BCA = 180-150= 30⁰

Angle APC = 60 + 45- 180

180-105 = 75°

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4. In the given figure, angle CEB = 120⁰. Calculate the measure of angle AED.

56°

2.92%

40°

5.26%

120°

88.89%

80°

2.92%

From the given figure, angle DEB = 180-120 = 600

Therefore, angle AED = 180-30 = 120°

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5. What is the measure of angle A in the given figure?

66°

4.55%

90°

88.31%

85°

3.9%

30°

3.25%

The internal angle B in the given triangle = 180-130 = 50⁰

The internal angle C in the given triangle = 180-140 = 40⁰

Therefore, in the given triangle, measure of angle A = 180 – (40 + 50)

180 – 90 = 90°

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6. Calculate the value of angle EDB when the remaining angles are given.

50°

71.88%

40°

19.38%

75°

3.75%

90°

In the given triangle ACE, vale of angle AEC = 180- (60+40)

= 180 – 100

=800

Also, the given angle DEB = 800 as it is directly opposite to angle AEC.

= In triangle DEB, value of angle EDB = 180 – (80+50)

=180 – 130

50°

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7. In the given figure, determine the value of angle RPB.

60°

13.38%

120°

81.69%

80°

2.82%

70°

2.11%

In the given triangle ABC, value of angle C = 180 – (60+90)

180 – 150 = 30⁰

Now, in the given triangle PCR, value of angle R = 90⁰

Value of angle CPR = 180 – (90+30)

180 – 120 = 60^°

Now, value of angle RPB = (180 - 60) = 120⁰

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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8. Calculate the area enclosed by ABDEF.

1312.5 cm2

74.4%

200 cm2

6.4%

350 cm2

4.8%

None of the above

14.4%

Area of ABDEF = area of ACEF – area of triangle BCD

= 50 x 30 – ((1/2)*15*25)

= 50 x 30 – 187.5

= 1500 – 187.5

= 1312.5 cm2

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9. What will be the area of the presented figure when all its sides are given?

11 cm²

20%

13 cm²

13.75%

10.72 cm²

50%

None of the above

16.25%

The presented figure can be divided into two triangles to calculate the area.

We can also label the given figure to identify and mark the 2 triangles.

Now the figure consists of triangles: ADC and triangle ACB.

The area of the given triangle can be calculated when we know the measure of length AC.

For this, in the given triangle, ADC,

AC² = AD² + DC²

AC² = 20² + 20²

AC =√400+400

AC = √800

AC = 28.28

Area of triangle ADC = ½*20*20

= 200 cm²

We also need the area of the triangle ABC

Area of the triangle when its three sides are given = √p(p-a)(p-b)(p-c)

Where p = (a+b+c)/2

P = (25+5+28.28)/2 = 29.14

Therefore, area of triangle = √29.14(29.14-25)(29.14-5)(29.14-28.28)

= √115.08

= 10.72 cm²

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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10. Determine the area of the given triangle.

25cm²

76.47%

15cm²

7.56%

10 cm²

6.72%

55cm²

9.24%

The solution is to rotate the triangle to bring the 10 feet side at the bottom.

Therefore, the area of the triangle =

Area=

= 25cm²

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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Heights and Distances – Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts
Perimeter Area and Volume – Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts
Coordinate Geometry – Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts
Venn Diagrams – Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts
Set Theory – Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts