Area, Volume and SA

​MGSE6.G.1 Find area of right triangles, other triangles, 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.

When do we need to find the area?

• Solving how much paint we need to paint a wall

• Solving how much flooring we need to cover a floor

• Solving how big a blanket needs to be to fit a bed

• Solving for a case to fit on a phone or tablet

Multiple Choice

What is the area of this shape?

• 8 square units

• 15 square units

• 14 square units

• 20 square units

Multiple Choice

What is the area of this shape?

• 10 square inches

• 20 inches

• 25 square inches

• 25 inches

Multiple Choice

Find the area

• 430 in²

• 215 in²

• 41.5 in²

• 1.5 in²

Area of Rectangles, Parallelograms & Squares

• Rectangles: L x W

• Parallelograms: B x H

• Remember, squares have all sides the same length!

Multiple Choice

Find the area of the triangle! (Don't forget to divide by 2!!)

• 17 units²

• 20 units²

• 10 units²

• 16 units²

Area of Triangles

Multiple Choice

Find the area of this triangle! (Don't forget to divide by 2!)

• 50 square inches

• 100 square inches

• 200 square inches

• 25 square inches

Multiple Choice

Find the area.

• 14 in²

• 18 in²

• 52 in²

• 28 in²

Area of a trapezoid

• To find the area use these three steps:

• Step 1: Add the two bases

• Step 2: Then multiply by your height

• Step 3: Divide by 2

Multiple Choice

Find the area.

• 108 cm sq

• 60 cm

• 432 cm sq

• 216 cm sq

Area of Different Quadrilaterals

Multiple Choice

Find the area of this square

• 49 inches

• 49 units

• 14 units²

• 49 units²

Multiple Choice

What is the area of a triangle with a base of 10 cm and a height of 14 cm?

• 24 cm squared

• 12 cm squared

• 70 cm squared

• 140 cm squared

Multiple Choice

Find the area:

• 13 in²

• 20 in²

• 26 in²

• 40 in²

Multiple Choice

Find the area:

• 84 m²

• 168 m²

• 112 m²

• 56 m²

Multiple Choice

Find the AREA of this figure.

• 160 square feet

• 160 feet

• abcdefghijklmnopqr stuvwxyz

• 1600 feet

Multiple Choice

Eriasia wanted to put down new tile in her bathroom. Her bathroom had a width of 10 ft and a width of 9 feet. How many square feet of tile should she buy?

• 90 square feet

• 19 square feet

• 38 square feet

Area of Composite Shape

Composite Shape

A composite shape is a shape that consists of more than one shape. To find the area you need to find the area of each shape and add the areas together.

Multiple Choice

Find the area of the composite figure

• 40

• 9

• 49

• 61

Multiple Choice

What is the area of the composite figure?

• 40 sq cm

• 65 sq cm

• 52.5 sq cm

• 25 sq cm

Multiple Choice

Determine the area of the composite figure shown below.

• 168 centimeters squared 

• 98 centimeters squared 

• 84 centimeters squared 

• 70 centimeters

Fill in the Blanks

Multiple Choice

• F

• G

• H

• J

Area of Circles

by Emily Phillips

Multiple Choice

What is circumference?

• space inside of a circle

• a set of points equidistant from one another

• distance around a circle

• crosses through the center point across a circle

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius

• Diameter

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius

• Diameter

Multiple Choice

How are the diameter and radius related?

• They're cousins

• Diameter is half of the Radius

• Radius is half of the Diameter

• They're brothers

Multiple Choice

What is the radius of this circle?

• 18

• 10

• 9

• 8

Multiple Choice

What is the diameter?

• 5 in

• 10 in

• 3.14 in

• 15.84 in

Multiple Choice

Find the area.

• $$6.28km^2$$  

• $$18.84yd^2$$  

• $$3.14yd^2$$  

• $$12.56km^2$$  

Multiple Choice

Find the area.

• $$200.96yd$$  

• $$50.24yd^2$$  

• $$200.96yd^2$$  

• $$74.16yd^2$$  

Multiple Choice

Find the area.

• $$56.52mi^2$$  

• $$28.26mi^2$$  

• $$9.42mi^2$$  

• $$254.34mi^2$$  

Multiple Choice

Find the area.

• $$28.26cm^2$$  

• $$113.04cm^2$$  

• $$12.56cm^2$$  

• $$3.14cm^2$$  

Multiple Choice

Find the area in terms of  $$\pi$$  

• $$10\pi in^2$$  

• $$5\pi in^2$$  

• $$100\pi in^2$$  

• $$25\pi in^2$$  

This is the formula to use if they give you the radius or diameter in order to find Circumference.

Multiple Choice

Alex has trained his puppy, Popper, to jump through a ring. According to Alex's measurements and calculations, the ring has a diameter of 3.5 feet. What is the ring's circumference (use 3.14 for pi)?

• 11.32 ft

• 12.25 ft

• 10.99 ft

• 8.75 ft

Multiple Choice

The diameter of a circle is 3 centimeters. What is the circumference?

• 11.5cm2

• 9.42 cm2

• unicorns are awsome

• 45.3 cm2

Multiple Choice

Find the circumference (to the nearest whole number)

• 88 in

• 44 in

• 116 square in

• None of the above

Multiple Choice

A circular swimming pool is 21 feet in diameter.
How many feet around is the pool?

• 10.5 ft

• 42 ft

• 65.94 ft

• 131.95 ft

Multiple Choice

The diagram below shows the radius of the circular opening of a drinking cup. Which of the following is closest to the circumference of the opening in centimeters?

• 12 cm

• 50 cm

• 25 cm

• 8 cm

​MGSE6.G.4 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = length x width x height and V = area of the base x height to find volumes of right rectangular prisms with fractional edges in the context of solving real-world math problems.

What is Volume

is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre.

Multiple Choice

What is the volume of this prism?

• 2 cubic in

• 12 cubic in

• 13 cubic in

Rectangular PRISMS

• V = Bh

• B is the AREA of the BASE

• Rectangle Area = bh

• B = 2x5

• V= (2x5) x 4

Multiple Choice

What is the volume of this prism?

• 6 cubic in

• 12 cubic in

• 24 cubic in

Multiple Choice

Lucia has a triangular prism that has a length of 6 cm, a width of 4 cm, and a height of 8cm. What is the volume?

• 96cm³

• 54cm³

• 80cm³

• 24cm³

Triangular PRISMS

• V = Bh

• B is the AREA of the BASE

• Triangle Area = 1/2bh

• B = (5x3)/2 = 7.5

• V= 7.5x10

Square Pyramids

Multiple Choice

What is the volume of this square pyramid?

• 112 in³

• 336 in³

• 11.2 in³

• 33.6 in³

Triangular Pyramids

Multiple Choice

Find the volume of the triangular pyramid.

• 22 cubic inches

• 33 cubic inches

• 66 cubic inches

• 44 cubic inches

Fill in the Blanks

Multiple Choice

Find the volume.

• 1,800 yd³

• 1,810 yd³

• 1,820 yd³

Multiple Choice

Which of the following answer choices displays the correct height to find the area of the base?

Multiple Choice

Which of the following answer choices displays the correct height of the prism?

Multiple Choice

Calculate the volume of the following triangular prism.

• 210 cm³

• 480 cm³

• 280 cm³

• 560 cm³

Fill in the Blanks

MGSE6.G.4 Represent three-dimensional figures 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.

By COLIN BROOME

Multiple Choice

Which figure will this net make?

• Rectangular Prism 

• Triangular Prism

• Triangular Pyramid 

• Cube

Multiple Choice

Which figure will this net make?

• Rectangular Prism 

• Triangular Prism

• Triangular Pyramid 

• Cube

Multiple Choice

How many faces does this shape have?

• 6

• 3

• 9

• 5

Multiple Choice

What is the Lateral Surface Area of this Rectangular prism?

• 50 cm²

• 600 cm²

• 90 cm²

• 50,000 cm²

Multiple Choice

What is the total surface area of this shape?

• 50 cm²

• 700 cm²

• 900 cm²

• 50,000 cm²

Multiple Choice

What is the surface area of the rectangular prism?

• 72 cm²

• 36 cm²

• 62 cm²

• 78 cm²

Multiple Choice

What shape is this?

• Triangular Prism

• Triangular Pyramid

• Rectangular Pyramid

• Rectangular Prism

Multiple Choice

What is the LATERAL surface area of the triangular prism shown.

• 140 cm²

• 280 cm²

• 120 cm²

• 448 cm²

Multiple Choice

Find the formula to help solve for the Surface Area of this Rectangular Prism.

• 5*8*7

• (2*5*8)+(2*7*5)+(2*7*8)

• 2(5+8+7)

• 1/2(5+7*8)

Multiple Choice

Find the area of the Triangular bases (do not add them). Just 1 Triangle!

• 240

• 135

• 120

• Still have no clue.

Open Ended

What is the difference between a prism and a pyramid?

• Prisms have two bases of the same shape with rectangular sides

• Pyramids have one base with triangular sides

Multiple Select

Choose the shapes that are prisms.

Multiple Choice

What is the surface area of the pyramid?

• 24 cm ²

• 84 cm ²

• 112 cm ²

• 64 cm ²