Math 1 · Unit 11 · Lesson 3

Perimeter and Area from Coordinates

Perimeter is the distance around a shape, so it is Lesson 1 for every side, then add. Area for a rectangle is length times width, both found by the distance formula. Area for a triangle is one half of base times height, and the height must meet the base at a right angle, which you check with slopes from Unit 4. For shapes without an easy height, draw a box around them and subtract the corner triangles.

About 45 minutes Check the height with slopes

The big idea

Perimeter is the distance around a shape, so it is the distance tool used once for every side, then added, with sides you can count counted and slanted sides measured with the right triangle underneath. Area is the flat space inside, in square units. A rectangle is length times width, both found with the distance formula when the rectangle is tilted. A triangle is one half of base times height, and the height has to meet the base at a right angle, so check the altitude with slopes first: a point is on the base if the slopes match, and the altitude is perpendicular if its slope is the negative reciprocal. When no easy height is there, box the shape along the grid lines and subtract the corner triangles.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Perimeter: every side, then addPerimeter is the distance all the way around a shape. 3Area: rectangles and trianglesArea is how much flat space a shape covers, in square units. 4The box methodWhen a shape has no easy base and height, use the box method . 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with perimeter as distance for every side, the pentagon, rectangle and triangle area, the altitude check, and the box method. Plus a worksheet with an answer key and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Midpoint, Meeting in the MiddleWhere is the middle? Next lesson: Proving Shapes with CoordinatesUse slope, distance, and midpoint together to prove what shape the points make. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Math 1 standards in this lesson: NC.M1.G-GPE.4 (compute perimeters of polygons and areas of triangles and rectangles using coordinates).