BASIC GEOMETRY WORD PROBLEMS

Problem 1 :

Two sides of a triangle are 7 and 13 centimeters. The perimeter of is 27 cm. Find the third side.

Solution :

Let a, b and c be the sides of the triangle.

a = 7, b = 13

Perimeter = Sum of all the sides

a + b + c = 27

7 + 13 + c = 27

20 + c = 27

c = 27 - 20

c = 7 cm

Problem 2 :

Find the area of the triangle given below.

Solution :

Base = 8 and height = 4

Area of the triangle = (1/2) x base x height

= (1/2) x 8 x 4

= 16 cm²

Problem 3 :

If a square has an area of 49 ft², what is the length of one of its sides? The perimeter ?

Solution :

Area of the square = 49 ft²

a² = 49

a² = 7²

a = 7

Length of one sides of the triangle is 7 cm.

Perimeter = 4a

= 4 (7)

= 28 cm

Problem 4 :

If a rectangle has a width of 4, how long must its length be so that the area is 36 ?

Solution :

Width of the rectangle = 4

Let l be the length of the rectangle.

Area of the rectangle = length x width

36 = 4 x l

l = 36/4

l = 9

Problem 5 :

If one angle of a right triangle is 70 degree. What are the other 2 angles ?

Solution :

Since it is a right triangle, one of the angle should be 90 degree. Let x be the third angle measure.

Sum of interior angles of the triangle = 180

70 + 90 + x = 180

160 + x = 180

x = 180 - 160

x = 20

Problem 6 :

Find b.

Solution :

Since it is right triangle, it holds the Pythagorean theorem.

5² = 4² + b²

25 = 16 + b²

25 - 16 = b²

b² = 9

b = 3

Problem 7 :

What is the diameter of the circle with an area of 16π ?

Solution :

Area of the circle = 16π

πr² = 16π

r² = 16

r = 4

d = 2(radius)

d = 2(4)

d = 8

So, the diameter of the circle is 8.

Problem 8 :

What is the circumference of the circle having an area of 25π (allow π = 3.14)

Solution :

Area of the circle = 25π

πr² = 25π

r² = 25

r = 5

Circumference of the circle = πd

= π(10)

= 20π

Problem 9 :

If the box has a height of 4 in, a length of 12 in and volume of 240 in³, what is the box's width.

Solution :

Height of the box = 4 inches, length = 12 inches

Let w be the width if the box.

Volume of the box = 240 in³

Volume of cuboid = length x width x height

4 x w x 12 = 240

w = 240/(4 x 12)

w = 5 inches

Problem 10 :

Find the volume of cylinder whose radius and height are 2 and 7 respectively.

Solution :

Volume of cylinder = πr²h

Radius = 2 and height = 7

Volume = (22/7) x 2² x 7

=  88