Question

question 18 of 20 (1 point) 1 question attempt: 1 of unlimited
(a) find the area of the following (in square units).
the dark rectangle (on the top): 21
the light rectangle (on the bottom): 7x
(b) give the area of the entire figure (in square units) in two different ways.
as a sum of two areas: 21 + 7x
as a product of the length and width: 21 + 7x

Explanation:

Step1: Find the sum of two areas

The sum of the areas of the two rectangles is \(21 + 7x\).

Step2: Find the product of length and width

The total height of the combined rectangle is \(x + 3\), and the width is \(7\). Using the formula for the area of a rectangle \(A=\text{length}\times\text{width}\), we have \(A = 7(x + 3)\). By the distributive property \(a(b + c)=ab+ac\), \(7(x + 3)=7x+21\).

Answer:

As a sum of two areas: \(21 + 7x\)
As a product of the length and width: \(7(x + 3)=7x + 21\)