7th GRADE GEOMETRY PRACTICE QUESTIONS

Question 1 :

The scale of a map is 1 1/4 inches = 100 miles. On that map, two cities are 4 1/8 inches actual distance between the cities?

a) 275 mi    b) 330 mi   c) 375 mi   d) 412.5 mi

Solution :

1  1/4 inches = 100 miles

5/4 inches = 100 miles

Dividing by 5/4 on both sides,

1 inch = 100/(5/4)

= 100(4/5)

1 inch = 80 miles

4 1/8 inches = 33/8 inches

Converting into miles,

33/8 inches = (33/8) x 80

= 33(10)

= 330 miles

So, option b is correct

Question 2 :

Find the value of x.

a) 18°    b) 90°   c) 36°     d) 48°

Solution :

The known angle measures in the triangles are 90 and 42.

Sum of interior angles of triangle = 180

Let x be the unknwon angle measure.

90 + 42 + x = 180

132 + x = 180

x = 180 - 132

x = 48

So, option d is correct.

Question 3 :

Which best describes a triangle with side lengths of 5 centimeters, 12 centimeters, and 13 centimeters?

a) unique triangle   b) no triangle    c) multiple triangles

d) nonexistent

Solution :

Let a, b and c are side lengths of the triangle.

a = 15 cm, b = 12 cm and c = 13 cm

Side lenghts of every triangle should satisfy triangle inequality theorem.

a + b > c, b + c > a and c + a > b

15 + 12 > 13, 13 + 12 > 15, 15 + 13 > 12

27 > 13, 25 > 15, 28 > 12

So, it will create a triangle. Option a is correct.

Question 4 :

Linda constructs a triangle with one side 5 inches long and another side 7 inches long. Which is NOT a possible length for the third side?

a) 3 inches    b) 6 inches    c) 11 inches    d) 12 inches

Solution :

Let a, b and c be the side lengths of triangle.

Let a = 5 inches, b = 7 inches and c be the missing side.

When c = 3

5 + 3 > 6, 7 + 3 > 5, 7 + 5 > 3

True

When c = 6

5 + 7 > 6, 7 + 6 > 5, 5 + 6 > 7

True

When c = 11

5 + 11 > 7, 5 + 7 > 11, 7 + 11 > 5

true

When c = 12

5 + 12 > 7, 12 + 7 > 5, 5 + 7 > 12

False

So, option d is correct.

Question 5 :

Charmaine constructs a triangle with angles measuring 65° and 38°. What must be true of the measure of the third angle in her construction?

a) It must measure exactly 77°

b) It must measure exactly 87°

c) It can have any measures less than 103°

d) It can have any measure greater than 27°

Solution :

Sum of interior angles of triangle = 180 degree

Let the third angle measure be x.

65 + 38 + x = 180

103 + x = 180

x = 180 - 103

x = 77

It must measure exactly 77°.

Question 6 :

Classify the following triangle according to its angles.

a) acute     b) isosceles    c) obtuse    d) equilateral

Solution :

By observing the figure, it is obtuse triangle.

Question 7 :

Classify the following triangle according to its sides.

a) scalene b) equilateral c) obtuse d) isosceles

Solution :

Based on the small indication, we know that it is isosceles triangle.

Question 8 :

A rose garden is circular. The diameter of the garden is 20 feet. Which is closest to the total area of the garden.

a) 56.52 ft²   b) 63.59 ft²   c) 314 ft²   d) 113.04 ft²

Solution :

Area of circle = πr²

Diameter = 20 ffeet

radius = 10 feet

= 3.14 (10)²

= 3.14 (100)

= 314 ft²

So, option c is correct.

Question 9 :

A circular swimming pool has a radius of 20 feet. The family that owns the pool wants to put up a circular fence that is 5 feet away from the pool at all points. Which is closest to the circumference of the fence they will need?

a) 94.2 ft   b) 75.5 ft    c) 157 ft    d) 188.4 ft

Solution :

Radius = 20 feet

Fecncing should be arranged at the distance of 5 units from the pool. So, radius to be covered is 25 feet.

Circumference of circle fencing = 2πr

= 2 x 3.14 x 25

= 50 x 3.14

= 157 ft

So, the length of fencing is 157 ft.

Question 10 :

You want to buy wheel covers for your bike to cut down wind resistance in order to go faster on your next race. Your bike has wheels with a circumference of 94.2 in. Find the number of square inches needed to cover the wheel.

a)   12.5 in²     b) 156.25 in²   c) 490.62 in²  d) 706.50 in²

Solution :

From the circumference given, we have to find the area.

2πr = 94.2 in

2 x 3.14 x r = 94.2

r = 94.2/(2 x 3.14)

r = 15

Area of circle = πr²

= 3.14 (15²)

= 3.14 (225)

= 706.5 in²

So, option d is correct.

Question 11 :

 What is the circumference of the circle below?

a) 210 cm  b) 66 cm  c) 131.88 cm   d) 181 cm

Solution :

Circumference of circle = 2πr

radius = 42/2 ==> 21 cm

= 2 x 3.14 x 21

= 131.88 cm

Question 12 :

At a train station, Track B crosses Track A and Track C, which are parallel to each other. Track A and Track B intersect at an angle of 150° as shown.

What is the m<x?

a) 30°      b) 50°     c) 150°     d) 180°

Solution :

track A and C are parallel, co-interior angles add upto 180

then, 150 + x = 180

x = 180 - 150

x = 30

So, option a is correct.

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