Module 5 Test Review

Now is a chance to review all of the great stuff you have been learning in Module 5!

– Area of Triangles– Area of Quadrilaterals– Area of Polygons– Shapes on the Coordinate Plane– Surface Area of Prisms– Surface Area of Pyramids

Area

Area:

The amount of square units contained within a plane, or a two-dimensional figure.

Area of a Rectangle - Review

Count each square unit within the rectangle. There are 21 square units. This method works if you have the shape on a grid.

Area can be found with or without a coordinate plane by multiplying the length by the width.7 × 3 = 21 square units.Therefore, the area of this rectangle is 21 units squared.

Area of a Triangle

Perpendicular Lines

"Perpendicular" means two lines that intersect to form a right angle (90 degrees).

Area of an Acute Triangle

Area of an Right Triangle

Total Area

• Using the same triangles from our earlier examples, use this example to see how you can find total area

The area of the acute triangle was 24 square inches. The area of the right triangle was 12 square inches.

Area of all three triangles = 24 + 12 + 12 = 48 square inches.

The area of the rectangle = 8 inches × 6 inches = 48 square inches.

QuadrilateralsA parallelogram is a four-sided polygon with two pairs of parallel and congruent sides.

You can identify which sides are congruent because you will see matching tick marks on them.

The rhombus is a parallelogram where all the sides are congruent.

A square is a special rhombus where all sides are congruent and perpendicular.

A kite has two pairs of congruent sides.

The important thing about the congruent sides is that they are adjacent (or next) to each other, not on opposite sides from each other.

A trapezoid is a quadrilateral in which one pair of opposite sides is parallel.You can see which sides are parallel because of the arrowhead.These sides are called bases of the trapezoid. The other sides can be of any length.

Area of Parallelogram

A parallelogram can be decomposed into two right triangles with a rectangle in between them. Drawing vertical lines from the corners to the base will create a height for the side triangles and a width for the rectangle. The important thing to notice is that the two side triangles are congruent.

Area of Parallelogram

To calculate the area of the parallelogram, add up the area of each shape created from the decomposition.

Area of a Rhombus

One way to compose a rhombus is by putting two congruent triangles together, so its decomposition would be just that.

Area of a Rhombus

Triangle A: The base is 8 inches, and the height is 4 inches.

A = bh

A =

A =

A = 16 in2

Triangle B:It will have the same area since it is congruent.

Area = triangle A + Triangle BA = 16 + 16A = 32 in2

Area of a Kite

A kite is composed of 4 right triangles.

Triangle A and B are congruent

Triangle C and D are congruent So to find the area of the kite, you need to just find the area of Triangle A and C, then double it.

Area of a Kite

Triangle A:The base is 6 ft., and the height is 7 ft.

Triangle C:The base is 16 ft., and the height is 7 ft.

Remember, triangle A and B are congruent, and triangle C and D are congruent.

Total Area = 2A + 2CA = 2(21) + 2(56)A = 42 + 112A = 154 ft2

Area of a Right Trapezoid

• How can you decompose this Right Trapezoid?

Area of a Right Trapezoid

Triangle: The base is 2 m, and the height is 6.5 m.

Rectangle: The length is 6.5 m, and the width is 5 m.

Total area = Triangle + rectangleA = 6.5 + 32.5A = 39 m2

Area of an Acute Trapezoid

• Can you use the decomposition method to find the area of this trapezoid?

Check your work

Polygons

Polygons can be classified as regular or irregular.

Regular polygon:A polygon that has all congruent sides and angles.

Irregular polygon:A polygon that does not have all congruent sides and angles

Examples of Polygons

Regular Polygons

How can we decompose this hexagon to find the area?

The key to decomposing and composing polygons is to use only shapes you are familiar with. You would not want to decompose this hexagon into a shape you do not have the dimensions for or that you do not know how to solve for the area of.

Regular Polygons

Method 2

Irregular Polygons

• Keep in mind there may be more than one way you can decompose an irregular polygon

• Here are two examples of how we can deconstruct this irregular polygon

Irregular Polygons

To calculate the area of this irregular polygon, all you need to do is calculate the area of each rectangle, then calculate the sum of the areas. Recall, the area of a rectangle A = l x w

Area of smaller rectangle 5 cm × 3 cm = 15 cm2

Area of larger rectangle 10 cm × 6 cm = 60 cm2

Total area of irregular polygon 15 cm2 + 60 cm2 = 75 cm2

Using a net to find Surface Area

• We can use the net of the rectangular prism to find the surface area.

• Drawing your net is the first step.

Using Nets to find the Surface Area

Next you want to find the area of each part:

To find the total area or Surface area, you add up the areas of the partsSA = 110 + 22 + 110 + 22 + 110 + 20 + 20 = 304 in2

Try It!

Use a net to solve for the surface area

Check your work

Surface of Triangular Prisms

Nico wants to stain his new skateboard ramp shown in the image with varnish

What is the total surface area of the prism?

Surface Area of a Triangular Prism

First, draw your net.

Now we need to find the area of each part.

Surface area of Triangular Prisms

Surface Area of Pyramids

We can use the nets of Pyramids to find the surface area.

Now, let's calculate the area of the square base. Area of the square base:8 in × 8 in = 64 in2

The last part in the calculation is to just determine the sum of all the faces. Total surface area of the pyramid:176 in2 + 64 in2 = 240 in2

Try it

Can you find the surface area of this pyramid?

Check your work

Total surface area:130 cm2 + 163.48 cm2 + 134 cm2 = 427.48 cm2

You have now had a chance to review all of the great stuff you learned in Module 5!

• Area of Triangles• Area of Quadrilaterals• Area of Polygons• Shapes on the Coordinate Plane• Surface Area of Prisms• Surface Area of Pyramids

Have you completed all assessments in module 5? Have you completed your Module 5 DBA?

Now you are ready to move forward and complete your module 5 test. Please make sure you are ready to complete your test before you enter the test session.