Equivalent Equations
Geometry Word Problems
Calculate the area or perimeter.
100

Distribute to write an equivalent expression 2(5x - 10)

10x - 20

100

Circle formulas (a = r2pi, C = 2rpi, D =2r)

Aaron the ant is walking around the edge of a soda can. The soda can has a radius of 4 cm. How far must Aaron walk to complete 1 lap? (Leave your answer in terms of pi)

C = 2rpi

C = 2*4cm*pi

C = 8pi cm

Aaron will walk 8pi cm. 

100

Formula (Area of Triangle = bh/2)

What is the area of a triangle with base of 4 cm, and height of 5 cm?

10 cm squared

200

Simplify the expression given by combining like terms. 15a - 13b + 5 -10a + 6b

5a -7b + 5

200
A square has a perimeter of 40ft. What is the area of the square?

100 square feet.

200

Formula (A = bh/2, P = a + b + c)

What is the area of a triangle with base of 7 cm, and height of 5 cm?

17.5 cm squared

300

Simplify the expression 2/5(15a - 30b + 5) -a.

5a - 12b + 2

300
Kipp needs to find the area of a triangle. He drew a rectangle around the triangle. The base of the triangle is equal to the width of the rectangle and the height of the triangle is equal to width of the rectangle. The rectangle has an area of 50 units squared. What is the area of the triangle?

25 units squared. 

300

Formulas (A = L*W, P = 2L + 2W)

What is the perimeter and area of a rectangle with length 12 cm and width 3 centimeters?

A = 36 cm squared

P = 30 cm

400

Simplify the expression 2/3(15a + 30b - 9) -a.

9a + 20b - 6

400

Circle formulas (a = r2pi, C = 2rpi, D =2r)
An artist is framing their work. Painting A is circular and has a diameter of 30 cm, and Painting B has a diameter of 21 cm. 

If the artist wants to frame the paintings with gold edging, how many centimeter will be needed to outline both paintings? ( Write in terms of pi)

C = 2rpi 

Painting A = 30pi cm

Painting B = 21pi cm

In total = 51pi cm

400

Circle formulas (a = r2pi, C = 2rpi, D =2r)

Biscuits are 3 cm in radius. What is their area? Answer in terms of pi.

9pi cm squared

500

Write the simplest form or each each below and state if they are equivalent to each other or not. 

¼(-20a + 32) − 9 and −5(a + 3) + 13

No, because 

1/4 (-20a + 32) -9 = -5a - 1 

-5(a +3) + 14 = - 5a - 2

-5a - 1 is not equal to -5a - 2

500

Circle formulas (a = r2pi, C = 2rpi, D =2r)

An artist is placing their painting on firm backgrounds as part of the framing process. The paintings and frames are circular. The painting is 12 cm in diameter, the frame needs to be 2 cm wider than the painting. How big does the frame need to be in cm2?

a = r2pi

d painting = 12cm, d frame = 14 cm

r frame = 7 cm

a frame= 7cm *7cm * pi

a frame = 49pi cm squared.

500

Circle formulas (a = r2pi, C = 2rpi, D =2r)

Frisbees cover an area of 144pi cm2. What is their diameter?

d = 24 cm

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