Find the area
of the figure.

Answer:

first the triangle

t area=b x h ÷2

=(5ft x 10.5ft)÷2

=26.25ft sq unit

second the rectangle

r area=L × b

=9ft × 7.5ft

=67.5ft sq unit

last the triangle

t area= b×h÷2

=(9ft×4.5ft)÷2

=20.25ft sq unit

Answer:

110.25 ft^2

Step-by-step explanation:

We can find the area of the figure by adding up the areas of three different shapes.

1) The right triangle

The formula for finding the area of a right triangle is: Base x Height x 1/2

The base in the right triable is 5 and the height is 9.

--> 5 x 9 x 1/2

--> 45/2

--> 22.5

2) The rectangle

The formula for finding the area of a rectangle is: Base x Height

The base is 7.5 and the height is 9.

--> 7.5 x 9

--> 67.5

3) The Isosceles Triangle (On the very right)

The formula for finding the area of a right triangle is: Base x Height x 1/2

The base of the triangle is 9, and the height is 4.5.

--> 9 x 4.5 x 1/2

--> 40.5/2

--> 20.25

Now that we know the areas of separate shapes, all we need to do is add them up!

22.5 + 67.5 + 20.25

= 110.25.

The area of the figure is 110.25 ft^2

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Module 06: Project Option 1
Instructions
Sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. After collecting only three shark’s teeth, Sarah decides to share the opportunity with her friend John. Sarah can find shark teeth twice as fast as John, but she can earn even more money with his help.


Sarah can use the expression 5(2j + 3 + j) to represent the amount of money they can earn.

Part 1: Writing Expressions
1. Write an expression that looks like Sarah’s expression: 5(2j + 3 + j). Replace the coefficients so that your expression is not equivalent. You may use any number that you choose to replace the coefficients. Be sure to leave the variables the same. For example, 8(3j + 7 + 3j) looks like Sarah’s expression but is not equivalent.


2. Translate the new algebraic expression you created in Question 1 to a verbal expression.


Part 2: Writing Equivalent Expressions
3. You will now use mathematical properties to create two expressions that are equivalent to the expression you created in Question 1. Make sure you show all steps in your work.
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b. Use the distributive property to create an equivalent expression.


4. Pick a number from 1 to 10. Use that number to verify your three expressions (the original, the one from 3a, and the one from 3b) are equivalent by substituting it into each expression. Show all your work for complete credit.

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