6th grade math help

Question

john built a wooden deck in his backyard, shown below.

A. What is the area of the deck? Show your work or explain your reasoning.

B. Sarah wants a deck with the same area as Jason's. However, she wants a rectangular deck. Give the dimensions of two different options of rectangular decks that Sarah can build. Justify your answers.

Type your answers in the box below.

Answer 1

Hi John,

For part a, we have to know that the shape shown is a trapezoid. The area of a trapezoid is given in the following formula:

A = (1/2)h(a+b),

where h is the height, a is base 1, and b is base 2.

Plugging our numbers into the formula, we have

A = (1/2)(8)(4+16)

A = (1/2)(8)(20)

A = (4)(20)

A = 80 ft^2

For part b, we want the same exact area but using a rectangular deck. The area of a rectangle is

A = lw,

where l is the length and w is the width.

We know that the area is 80 ft^2. We need two numbers that when multiplied together give us 80.

80 = lw

Let's say that l = 20 and w = 4. This would give us 20*4=80.

We can also use l = 5 and w = 16. This would give us 5*16=80.

There are a lot of choices to choose from, but you only needed two!

Hope this helps!