1.4 Perimeter and Area in the Coordinate Plane

​Unit 1, Lesson 1.4
Perimeter and Area in the Coordinate Plane

​

" It always seems impossible until it's done"

-Nelson Mandela

In this lesson, you will

1. use the coordinates of the vertices of a polygon to

find the necessary dimensions for finding the
perimeter and area

2. use the measurements of various polygons for

finding the perimeter and area

The area is the amount of surface enclosed by a perimeter (the
amount of space it takes to cover a polygon) and is measured in

square units.

Different types of polygons have different formulas for area.

Audio Response

Video (Box Method)

Open Audio Recorder

Your Tools

Multiple Choice

What is the area of the rectangle?

• 28 units squared

• 45 units squared

• 33 units squared

• 19 units squared

Multiple Choice

You design a tree house using a coordinate plane. You plot the vertices of the floor at J (2, 1), K (2, 8), L(9, 8), and M (9, 1). The coordinates are measured in feet. What is the area of the tree house?

• 28 feet²

• 49 feet²

• 56 feet²

• 64 feet²

Multiple Choice

What is the area of the rectangle shown on the coordinate grid?

• 15 square units

• 24 square units

• 30 square units

• 50 square units

Fill in the Blank

What is the area of square ABCD?

USE THE DISTANCE FORMULA AND REMEMBER A=bh

Multiple Choice

Square ABCD has vertices A(-2,-3), B(4, -1), C(2, 5), and D(-4, -3). What is the area of the square?

• $$2\sqrt{10}$$

• $$4\sqrt{10}$$

• 40

• 20

Multiple Choice

What is the perimeter of the shape?

• 20 units

• 12 units squared

• 22 units

• 32 units squared

Multiple Choice

What is the perimeter of the rectangle? (Round to the nearest tenth)

• 18

• about 23.6

• about 25.1

• about 21.6

Multiple Choice

What is the perimeter (in units) of the triangle formed by the points (-3,1), (-3,5), and (4,1)?

• 65

• 8.06

• 14

• 19.06

Multiple Choice

What is the area of this figure?

• 7 units²

• 15 units²

• 7.5 units²

• 15.5 units²

Multiple Choice

Given ΔBUG as shown with

B(-3,-1), U(-3,3) and G(4,1).

Find the area of triangle BUG.

• 28 square units

• $$\sqrt{28}$$ square units

• 14 square units

• 12 square units

Fill in the Blank

Given ΔNUF as shown with N(1,3),

U(5,6), and F(4,-1).

Find the area of right ΔNUF.

Multiple Choice

Find the exact area of  $$\Delta RST$$  .

HINT: USE THE DISTANCE FORMULA TO FIND THE BASE AND HEIGHT OF THE TRIANGLE. $$Area\ of\ a\ Triangle=\frac{\left(base\right)\times height}{2}$$  

• $$9\sqrt{3}+15$$  

• $$9\sqrt{5}+15$$  

• 45

• 90

Multiple Choice

Find the perimeter. Round to the nearest tenth, if necessary.

• 20

• 18.5

• 11

• 33.5