Coordinate Plane & Area

Coordinate Plane

100

Determine wether the following shapes are polygons. If they are, classify them. 

1. 

2. 

3. 

1. Yes; a pentagon

2. No, it is not closed

3. No, it does not contain 3 or more line segments

200

Reflect these points across the x-axis:

A(3,-2)

B(1,4)

C(8,8)

What are the new coordinates?

The new coordinates after reflection are: 

A(3,2)

B(1,-4)

C(8,-8)

300

Graph the points A(-3,4), B(-4,-2), C(1,-2), D(0,4). Connect A to B to C to D to A. What names (at least 2) can you use to describe this figure?  

- Polygon

- Quadrilateral 

- Trapezoid 

400

Find the area of the shaded region.

We need to subtract the area of the small rectangle from the large one.

A_{Small} = 2\times7=14 \ units ^2

A_{Larg e} = 4\times12=48 \ units^2

Thus, the shaded region has an area of

48-14=34 \ units^2

 

Coordinate Plane

100

Each of these points represents an object. Find the distance between these 2 points on the coordinate plane. Note, each unit represents 10 meters. 

Counting the boxes, we see the 2 points are 6 units away. Since each unit represents 10 meters, the objects are 60 meters away.

200

Reflect these points across the y-axis:

A(3,-2)

B(1,4)

C(8,8)

What are the new coordinates?

A(-3,-2)

B(-1,4)

C(-8,8)

400

The coordinates of two vertices of a right triangle are A(-3,5) and B(2,4). What are the 2 possibilities for coordinates of vertex C if the figure formed is a right triangle? 

Possibility #1

C=(-3,4)

Possibility #2

C=(2,5)

Area of Triangles, Parallelograms, Trapezoids, Composite shapes

100

Find the area of these parallelogram's in square units. 

#1

#2

A=b\cdoth

where b is the base and h is the height.

#1

A=12*5.5=66 \ units^2

#2

Make sure to first find the total length of the base (which is 9+2=11).

Now, 

A=11\cdot13=143 \ units^2

200

Find the area of the following triangles:

#1

#2 

For a triangle, 

Area=1/2b\h

#1 

A=1/2(8\ yd) (8\ yd)=32\ yd^2

#2

A=1/2(4\ ft) (9\ ft)=18\ ft^2

300

Find the area of the following composite figure:

We can split this into two rectangles.

Area of 1st rectangle: 

A=4\times5=20 \ units^2

Area of 2nd rectangle:

A=8*2=16 \ units^2

So, the total area is 

20+16=36 \ units ^2

400

Find the area of the following trapezoids:

#1

#2

A=1/2h(b_1+b_2)

#1

A=1/2(9)(15+7)=1/2(9)(22)

Simplifying, 

A=11\times9=99 \ meters ^2

#2

First, identify 

h=4, b_1=8, b_2=6

Now, using the above formula, 

A=1/2(4)(8+6)=2(14)=28 \ units^2

500

A parallelogram's height is three times its base. If it has an area of 108 square feet, what are the lengths of its base and height? 

Let x = base

Then, 3x = height

Area = base x height = 

x\times3x=3x^2

Since we are given that the area is 108 square feet, we know that:

3x^2=108

Dividing both sides by 3, we see that:

x^2=36

Now, if you recall what squared means, you will realize that

6^2=36

 so, x=6. 

x=6 ft is the length of the base. 

As we defined above, 3x is the height, so it is 

3(6)=18ft

Area of Triangles, Parallelograms, Trapezoids, Composite shapes

100

A right triangle has an area of 20 square meters, and a base length of 8 meters. What is its height?

A=1/2bh

Substituting the known values:

20=1/2(8)(h)

Simplifying:

20=4h

Dividing by 4:

h=5 \ meters

200

One base of a trapezoid measures 12 meters, and the other base measures 8 meters. If the area is 144 square meters, what is the height of the trapezoid?

A=1/2h(b_1+b_2)

Substituting,

144=1/2h(12+8)

144=1/2(20)(h)=10h

Dividing by 10,

h=144/10=14.4 \ meters 

300

The area of a trapezoid is 65 square feet. If the height is 10 ft, what is the sum of the lengths of the bases?

A=1/2(h)(b_1+b_2)

We want to find the sum of the lengths of the bases, which is 

(b_1+b_2)

Using our formula, we have that:

65=1/2(10)(b_1+b_2)=5(b_1+b_2)

Dividing both sides by 5, we see that:

b_1+b_2=65/5=13 \ ft

So, the sum of the lengths of the bases is 13 ft. 

400

Find the area of the following composite figure.

This can be split into a rectangle and a trapezoid.

The area of the rectangle is: 

A=12\times10=120 \ units^2

The area of the trapezoid is:

A=1/2(16)(10+24)=8(34)=272 \ units^2

So, the total area is:

120+272=392 \ units^2

500

Find the area of the following composite figure. 

Labeling the figure, it now looks like the figure above. Note, the 3rd side of the triangle is 3 inches, and the 5 inches is not necessary to solve the problem. 

So, the total area is 84 square inches. 

Surprise me

100

1. What is the distance between A(3,1) and B(3,8)

2. What is the distance between C(2,-1) and D(-4,-1)

1. 7 units 

2. 6 units

200

The Shanghai World Financial Center is one of the tallest buildings in the world. It features a large trapezoidal opening to allow wind to pass through. The opening is about 35 meters tall. It is about 40 meters along the bottom and 50 meters along the top. What is the approximate area of the opening?

A=1/2h(b_1+b_2)

Substituting the numbers, we get:

A=1/2(35)(40+50)

Simplifying:

A=1/2(35)(90)=1/2(90)(35)

Solving:

A=45\times35=1,575 \ m^2

300

A blueprint of a rectangular pool is shown. 

 

What are the area and perimeter of the pool? 

The dimensions of the pool are 23 x 12.

Area=bh=23\cdot12=276 \ units^2

Perimeter=23+23+12+12=70 \ units ^2

400

A trapezoid's larger base is 4 times the length of its shorter base. If it has an area of 70 square feet, and a height of 4 ft, what is the length of the shorter base?

b_1=

shorter base

4b_1=

longer base

So, 

A=1/2h(b_1+b_2)

70=1/2(4)(b_1+4b_1)

Simplifying:

70=2\cdot5b_1=10b_1

Dividing by 10, 

b_1=70/10=7

So, the shorter base is 7 ft. 

500

Find the area of the shaded figure below.

Hints

-You do not need all the numbers 

-You should use the subtractive method (big area - small area)

So, the area is 313 square centimeters.