CCGPS Unit 5 Overview

Area and Volume

MCC6.G.1

Find the area of right triangles, other triangles,

special quadrilaterals, and polygons by

composing into rectangles or decomposing into triangles and other shapes; apply these

techniques in the context of solving real-world and mathematical problems.

Examples: • Area of Right Triangles• Area of Triangles• Area of Squares• Area of Kites• Area of Parallelogram• Area of Trapezoid• Real-World Problems with

Area

Vocabulary Words• Right Triangle• Square• Kite• Parallelogram• Trapezoid• Area

Right TriangleA triangle that has exactly one 90◦ angle

Base

ALTITUDE

AREA of a Right TriangleA = ½BH

3 ft

4 ft

Substitute the values into the equation.• b = 3ft• h = 4ft

We are solving for A.

A = ½ (4 ft)(3 ft)

A = ½ (12 ft2)

A = 6 ft2

AREA of a Right TriangleA = ½BH

6.2 ft

8.4 ft

We are solving for A.

A = ½ (8.4 ft)(6.2 ft)

A = ½ (52.08 ft2)

A = 26.04 ft2

TriangleA polygon having three sides.

Base

ALTITUDE

AREA of a TriangleA = ½BH

6 ft

4 ft

We are solving for A.

A = ½ (6 ft)(4 ft)

A = ½ (24 ft2)

A = 12 ft2

AREA of a Parallelogram

9 ft

6 ft

We are solving for A.

A = ½(6 ft)(9 ft) + ½(6 ft)(9 ft)

A = ½(54 ft2) + ½(54 ft2)

A = 27 ft2 + 27 ft2

A = 54 ft29 ft

AREA of a Parallelogram

A = BH9 ft

6 ft

We are solving for A.

A = (6 ft.)(9 ft.)

A = 54 ft2

AREA of a Rhombus

A = BH

We are solving for A.

A = (4 ft)(3 ft)

A = 12 ft2

4 ft

4 ft3 ft

A Rhombus is a four-sided Polygon where all sides have

equal length (It looks like a someone sat on a square)

4 ft.

4 ft.

AREA of a RectangleA = L x W

10 ft

We are solving for A.

A = (15 ft)(10 ft)

A = 150 ft2

15 ft

AREA of a SquareA = s2

10 ft.

We are solving for A.

A = (10 ft)(10 ft)

A = 100 ft2

10 ft.

AREA of a Kite

12 in.

Suppose you were asked to find the area of this kite. Using what we already know about triangles, how can we find the area of the kite?

We are solving for A.

A = ½(24in12 in) + ½(24 in36 in)

A = ½(288 in2) + ½(864 in2)

A = 144 in2 + 432 in2

A = 576 in2

24 in.

36 in.

AREA of a TrapezoidHow can we find the area of this trapezoid?

We are solving for A.

A = ½(12 in24 in)½(12 in 24 in)+ (12 in 24 in)

A = ½(288 in2)½(288 in2)+ (288 in2)

A = 144 in2 + 144 in2 + 288 in2

A = 576 in2

24 in.

12 in.

36 in.12 in. 12 in. 12 in.

Mr. and Mrs. Brady purchased this home in Marietta, Georgia. Mrs. Brady is tired of looking at the brown dirt patch in the median of the road in front of their home. She has asked her husband to plant something in that area which will give it a more attractive curb appeal. Mr. Brady knows that the soil will need to be treated with fertilizer in order for it to be able to grow beautiful flowers. Mr. Brady needs to find the area of the ground to be treated. He has provided the length of two sides that make a right angle for you to use to determine the area. One side is twenty five feet. The other side is 9 feet. What is the Area?

25 feet9 feet

Area = ½ Base x Height

A = ½ (9 feet) x (25 feet)

A = ½ (225 ft2)

A = 112.5 ft2

The Beijing National Aquatics Center has request your help. They require a cover for the Olympic swimming pool that is housed within this beautiful building. The pool has eight lanes that are each 2.5 meters wide. The length of each lane is 50 meters long. How long will the cover need to be if you wish to cover only the surface of the pool?

Area = Base x Height

A = (2.5 meters) x (50 meters)

A = (125 meters2)

If one lane is 125 m2. and we have eight lanes than we need to multiple the area of one lane by the total number of lanes 8

125 m2 x 8 = 1000 m2

MCC6.G.2

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate

fraction edge lengths, and show that the volume is the same as it would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and

V = Bh to find the volumes of right rectangular prisms with fractional edge lengths in the

context of solving real-world and mathematical problems.

Examples: • Use unit cubes to pack a

right rectangular prism with fractional edge lengths

• Find the volume of right rectangular prisms using the volume formulas

• Real-world problems Vocabulary Words• Prism• Right Rectangular Prism• Edge• Base of a Prism• Volume• Unit Cubes

http://learnzillion.com/lessons/1064-find-the-volume-of-a-rectangular-prism-with-fractional-edge-lengths

Volume with fracti onal Lengths

1/2 in.

2 units

2 units

1.5 units

Find the volume of a rectangular prism with fractional edge lengths

You cannot use a whole unit block as a visual because when you try the block will extend past the boundary of the original shape.

To fill a fractional side we will need a fractional unit cube.

1 unit

1 unit

1 unit

Now we can insert the ½ unit blocks onto the bottom row of our figure .

6 x ½ = 3 whole unit blocks on bottom row6 X ½ = 3 whole unit blocks on the top row3 + 3 = 6 total whole unit blocks

MCC6.G.4

Represent three-dimensional figures using

nets made up of rectangles and triangles using nets made up of

rectangles and triangles, and use the nets to find

the surface area of these figures. Apply these

techniques in the context of solving real-world and mathematical problems.

Examples: • Nets of triangular prisms• Nets of rectangular prisms• Nets of square pyramids• Nets of rectangular

pyramids• Surface area of each of the

prisms and pyramids• Real-world problems

Vocabulary Words• Nets• Triangular Prisms• Pyramid• Surface Area

SURFACE AREA of a Square Pyramid

By looking at a net of this square pyramid determine the surface area. Surface are of the square in the middle:

SA = (5 ft.)(5 ft.)

SA = 25 ft2

Surface are of one of the triangle segments:

SA = ½ (5 ft.)(6 ft.)

SA = 15 ft2

6 ft.

5 ft.

By looking at a net of this square pyramid determine the surface area. Surface are of the square in the middle:

A = 25 ft2

Surface are of one of the triangle segments:

A = 15 ft2

Total Surface Area: 1 square & 4 Triangles

A = 25 ft2 + 4 (15 ft2)

A = 85 ft2

SURFACE AREA of a Rectangular Prism

By looking at a net of this rectangular prism determine the surface area. Similar rectangles are labeled. Surface area of the rectangle A.

SA = (3 ft.)(1 ft.)

SA = 3 ft2

1 ft. 3 ft.

5 ft.

3 ft.

A

A

B C BC

By looking at a net of this rectangular prism determine the surface area. Similar rectangles are labeled. Surface area of the rectangle B.

SA = (3 ft.)(5 ft.)

SA = 15 ft2

By looking at a net of this rectangular prism determine the surface area. Similar rectangles are labeled. Surface area of the rectangle C.

SA = (5 ft.)(1 ft.)

SA = 5 ft2

By looking at a net of this rectangular prism determine the surface area. Similar rectangles are labeled. Surface area of all six rectangles.

Rectangle A - SA = 3 ft2

Rectangle A - SA = + 3 ft2.Rectangle B - SA = + 15 ft2

Rectangle B - SA = + 15 ft2

Rectangle C - SA = + 5 ft2

Rectangle C - SA = + 5 ft2

Total = SA = 46 ft2