Geometric Application Problems Lesson

Ware County High School





Algebra Concepts and Connections
Spring 2026

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​Geometric Application Problems

I can apply the distance and midpoint formulas and slope of parallel and perpendicular line segments to solve real-world problems.

​​Learning Target

​I can use the distance and midpoint formulas to solve real world problems.

I can use parallel and perpendicular slopes to solve real world problems.

​​Success Criteria

​Example 1) A singles tennis court is a rectangle 27 feet wide and 78 feet long. Suppose a player at corner A hits the ball to her opponent in the diagonally opposite corner B. Approximately how far does the ball travel, to the nearest tenth of a foot?

​Example 2) A map of an amusement park is shown on a coordinate plane, where each square of the grid represents 1 square meter. The water ride is at (-17, 12), the roller coaster is at (26, -8) and the Ferris Wheel is at (2, 20). Find each distance to the nearest tenth of a meter.

Math Response

Your Turn 3) A doubles tennis court is a rectangle 36 feet wide by 78 feet long. If two players are standing in diagonally opposite corners, about how far apart are they, to the nearest tenth of a foot?

Type answer here

Correct Answer: 85.9

Deg^°

Rad

Example 5) To get from one side of the pond to the other, Conrad must walk 24 meters south and 31 meters east. To the nearest meter, how many less meters would it take if it were possible to go directly across the pond?

​When in doubt, draw it out!!

Math Response

Your Turn 4) Using the map of the Sacramento Zoo, determine the total distance you would walk if you started at the jaguar exhibit, then walked directly to the tiger exhibit, and then you walked to the otter exhibit. (Each square on the map represents 1 square meter.)

Type answer here

Correct Answer: 13.9

Deg^°

Rad

Math Response

Your Turn 7) An electrical wire starts at point A and runs 80 yards due north, then turns and runs 95 yards dues east to point B. How much farther is it to string the wire this way rather than the shortest distance across the lake? Round your answer to the nearest tenth. (Hint: how much farther also means what is the difference.)

Type answer here

Correct Answer: 50.8

Deg^°

Rad

​Example 6) A farmer would like to build a fence around this animal farm property. The farmer needs to create a fence with posts halfway between points A and B, halfway between points B and C, halfway between points C and D, and halfway between points D and A. (Each square on the graph represents one square meter.)

​a) Where would he place the fence posts for each side of the fence?

​Example 6) A farmer would like to build a fence around this animal farm property. The farmer needs to create a fence with posts halfway between points A and B, halfway between points B and C, halfway between points C and D, and halfway between points D and A. (Each square on the graph represents one square meter.)

​b) How much fencing does he need to fence the property?

​Example 6) A farmer would like to build a fence around this animal farm property. The farmer needs to create a fence with posts halfway between points A and B, halfway between points B and C, halfway between points C and D, and halfway between points D and A. (Each square on the graph represents one square meter.)

c) What is the area of the animal farm?

Open Ended

Your Turn 8A) Finlee is needing to put around a space in her yard to create a dog pen. The space that she wishes to fence in is shown below where each unit on the graph represents one foot. Finlee needs to place a post half way between each corner of the fence. Where will these posts go? Ex. AB=(x,y)

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