Question

The Sawyers are adding a family room to their house. The dimensions of the room are 26 by 28 feet. Show how to use the Distributive Property to mentally calculate the area of the room

Answer 1

The area of the room would be 728

Since the dimensions are 26 by 28 feet, you can break down 26 into 20 and 6, and 28 into 20 and 8.
Then, you can use the distributive property,
which states that a(b + c) = ab + ac.
So, you can mentally calculate the area of the room as follows:
Area = (20 + 6) * (20 + 8)
= 20 * 20 ÷ 20 * 8 + 6 * 20 + 6 * 8
= 400 + 160 + 120 + 48
= 728 square feet

Answer 2

728 square feet.

Explanation:

The area of a rectangle is the length times the width.

So, the area of the Sawyers' family room is 26 feet times 28 feet.

We can use the distributive property to mentally calculate this area as follows:

`\sf (26 feet)(28 feet) = 26 feet * (20 feet + 8 feet)`

Using the distributive property, we can distribute the 26 feet to each of the terms inside the parentheses and simplify:

This gives us:

`\begin{aligned} \textsf{ Area } &\sf= (26 feet * 20 feet) + (26 feet * 8 feet)\\\\ &\sf = 520 feet + 208 feet \\\\ &\sf = 728 feet \end{aligned}`

Therefore, the area of the Sawyers' family room is 728 square feet.