Perimeter is the distance around an object. It is useful for finding out things such as how much fencing you need for your yard, or baseboard for your room. To find the perimeter of an object, you can add up each side.

Here’s an example:

Aelfric and Oslafa want a new fence around their sheep’s pasture. They want it to be 5’ feet tall. The pasture is 50’ by 40’, and they’ll need a post every six feet to secure the fencing. The posts will cost $13.50 each, and the 5’ fencing is $8.50 per foot.

Problem 1. Calculate the perimeter of their pasture.

Solution: Perimeter = 2 x 50ft + 2 x 40ft, P = 180ft

Problem 2. How many posts do they need?

Solution: 180ft ÷ 6 posts = 30 posts

Problem 3. How much will the materials for the fence cost?

            Solution:

a) 30 posts x $13.50 = $405
b) 180ft x $8.50 = $1,530
c)Total: $405 + $1,530 = $1,935

Part I

This is Daedalus and Eudoxia’s new house—it’s alright, but they think it could use some baseboard in each of the rooms.

1. Find the perimeter of the family room, ignoring the doors.   _______________

2. There are three doors in the family room: the bedroom and entrance doors are 3’ wide, and the front porch door is 5’. Calculate the perimeter again: ________________

3. The baseboard is $7.89 per foot. How much will it cost to buy the baseboard for the family room? _______________

4. Find the perimeter and cost of the baseboard for the other rooms. The doors are all 3’ wide.

a) Bedroom            ______________    _________________

b) Laundry Room ______________    _________________

c) Entrance            ______________    _________________

5. How much will the baseboard cost in total?  ____________________

 

Part II

Since they are having problems with Gauls invading the area, Tiberius and Gaius want a trench around their small fort. Here are the dimensions of their fort:

1. Calculate the fort’s perimeter.   ____________________

2. They want a trench going all around the fort and dug 2 feet away from the walls. Calculate the perimeter of the trench. ________________

3. The cost of the trench will be $4.50 per foot. They’ll need a new gate too, after some Gauls broke the last one, which is going to cost $60. Calculate the cost of the trench and new gate. ___________________

4. Tiberius and Gaius hired Rufus and his crew to dig the trench. He charges $40 per hour and estimates it will take them 10 hours to dig. How much will the labour cost?  __________________

5. All together, how much will their project cost? _________________