Basic Geometry Practice Questions

High School geometry questions similar to what you will find on a standardized test.

Practice Questions

LineAngle1

1. What is measurement of the indicated angle assuming the figure is a square?

a. 45o
b. 90o
c. 60o
d. 30o

LineAngle2

 

 

 

 

 

2. What is the sum of all the angles in the rectangle above?

a. 180o
b. 360o
c. 90o
d. 120o

Line3

3. What is the measurement of the indicated angle?

a. 45o
b. 90o
c. 60o
d. 50o

Line4

4. If the line m is parallel to the side AB of ?ABC, what is angle a?

a. 130o
b. 25o
c. 65o
d. 50o

PerimeterArea

 

 

 

 

 

 

 

 

 

5. What is perimeter of the above shape?

a. 12 cm
b. 16 cm
c. 6 cm
d. 20 cm

PerimeterArea2

 

 

 

 

 

 

 

 

 

6. What is (area of large circle) – (area of small circle) in the figure above?

a. 8 п cm2
b. 10 п cm2
c. 12 п cm2
d. 16 п cm2

Perimeter5

7. What is perimeter of ?ABC in the above shape?

  1. 25.5 cm
  2. 27 cm
  3. 30 cm
  4. 29 cm

PerimeterArea6

 

 

 

 

 

 

 

8. What is the volume of the figure above?

a. 125 cm3
b. 875 cm3
c. 1000 cm3
d. 500 cm3

PerimeterArea8

9. What is the volume of the above solid made by a hollow cylinder with half in size of the larger cylinder?

a. 1440 п in3
b. 1260 п in3
c. 1040 п in3
d. 960 п in3

Answer Key

1. B
The diagonals of a square intersect perpendicularly with each other so each angle measures 90o
x =90o

2. B
a+b+c+d = ?
The sum of angles around a point is 360o   a+b+c+d = 360o

3. C
The sum of angles around a point is 360o
d+300 = 360o
d = 60o

4. D
Two parallel lines(m & side AB) intersected by side AC
a= 50o (interior angles)

5. B
The square with 2 cm side common to the rectangle apart from 4cm side
Perimeter = 2+2+2+4+2+4 = 16 cm

6. C
In the figure, we are given a large circle and a small circle inside it;
with the diameter equal to the radius of the large one. The diameter of the
small circle is 4 cm. This means that its radius is 2 cm. Since the diameter
of the small circle is the radius of the large circle, the radius of the large
circle is 4 cm. The area of a circle is calculated by: пr2 where r is the
radius.  Area of the small circle: п(2)2 = 4п Area of the large circle: п(4)22 = 16п

The difference area is found by:
Area of the large circle – Area of the small circle = 16п – 4п = 12п

7. D
Perimeter of a shape with two squares and triangle ABC.
Perimeter = 8.5+8.5+6+6
Perimeter = 29 cm.

8. C
Large cube is made up of 8 smaller cubes of 5 cm sides.
Volume = Volume of small cube x 8
Volume = (5 x 5 x 5) x 8, 125 x 8
Volume = 1000cm3

9. B
Volume= Volume of large cylinder – Volume of small cylinder
(Volume of cylinder = area of  base x height)
Volume
= (п 122x 10) – (п 62x 5), 1440? – 180п
Volume= 1260п in3

See also our tutorial on Complex Shapes

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    7 Comments

  1. angel
    March 4, 2017
    Reply

    answer to question five should be 18, you forgot to include the 2cm outer side of the rectangle

    • Brian
      March 7, 2017
      Reply

      Divide the figure into a square and a rectangle – perimeter of the square – 3 X 2 = 6 note 3 sides are included in the perimeter. Upper rectangle 2 X 4 = 8 + 2 = 10 total perimeter = 10 + 6 = 16

    • yo
      August 23, 2018
      Reply

      what angel said is so true, i cant believe u guys made such a silly mistake

      • Brian
        August 23, 2018
        Reply

        Try again – the question asks for the PERIMITER – 3 sides of the square – 2 + 2 + 2 = 6; 2 sides of the rectangle – 4 + 4 = 8; 1 side of the rectangle (top) = 2
        6 + 8 + 2 = 16

  2. Odey Grace
    June 1, 2017
    Reply

    Please in no 6 ,42 -22 is 20,so how comes about 16 and how did u get 122 in no 10

    • Brian
      June 3, 2017
      Reply

      The answers are correct – I have updated and expanded the solutions – also the п symbol wasn’t displaying properly – thanks!

  3. Joe
    July 5, 2018
    Reply

    Love this. Super helpful!

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