Question

1. kyle and his father are planning to repaint one wall in kyle’s bedroom. one can of paint covers 100 square feet. which expression represents how kyle and his father can decompose to find the area of the wall? image of a wall with 10 feet and 18 feet marked a. ( 10 \times 10 + 10 \times 8 ) b. ( 10 \times 8 + 18 \times 8 ) c. ( 10 \times 10 + 8 \times 8 ) d. ( 10 \times 18 + 10 \times 8 ) b. what is the total area of the wall to be painted? 16 answer: ____ sq __ image of a composite figure with units marked 17 answer: __ sq ____ image of another composite figure with cm marked

Explanation:

Part a:

Step1: Analyze the wall's decomposition

The wall can be decomposed into two rectangles. One way is to split the 18 - foot length into 10 and 8 (since \(10 + 8=18\)) and keep the height as 10 feet? Wait, no, looking at the options, option A is \(10\times10 + 10\times8\). Let's check: if we split the wall into two rectangles, one with dimensions \(10\times10\) and another with \(10\times8\), because \(10 + 8 = 18\) (the total length) and the height is 10. So the area of the first rectangle is \(10\times10\) and the second is \(10\times8\), and the total area is the sum of these two.

Step2: Evaluate other options

• Option B: \(10\times8+18\times8\) would imply a height of 8, but the height of the wall is 10, so this is incorrect.
• Option C: \(10\times10 + 8\times8\) is adding areas of two squares, which doesn't match the wall's dimensions.
• Option D: \(10\times18+10\times8\) would be double - counting or incorrect decomposition.

Step1: Use the correct expression from part a

From part a, the expression is \(10\times10+10\times8\).

Step2: Calculate each term

First term: \(10\times10 = 100\). Second term: \(10\times8=80\).

Step3: Sum the terms

Total area \(=100 + 80=180\) square feet.

Answer:

A. \(10\times10 + 10\times8\)

Part b: