Question

the following figure is a rectangle made up of two smaller rectangles. (a) find the area of the following (in square units). the light rectangle (on the top): the dark rectangle (on the bottom): (b) give the area of the entire figure (in square units) in two different ways. as a sum of two areas: as a product of the length and width:

Explanation:

Part (a)

Light Rectangle (Top)

Step1: Recall rectangle area formula

The area of a rectangle is given by \( A = \text{length} \times \text{width} \). For the light rectangle, the length is 6 and the width is \( x \).

Step2: Calculate the area

Using the formula, the area \( A_{\text{light}} = 6 \times x = 6x \).

Dark Rectangle (Bottom)

Step1: Recall rectangle area formula

The area of a rectangle is \( A = \text{length} \times \text{width} \). For the dark rectangle, the length is 6 and the width is 7.

Step2: Calculate the area

Using the formula, the area \( A_{\text{dark}} = 6 \times 7 = 42 \).

Part (b)

As a sum of two areas

Step1: Sum the areas of the two rectangles

The total area is the sum of the area of the light rectangle and the dark rectangle. We know \( A_{\text{light}} = 6x \) and \( A_{\text{dark}} = 42 \), so the total area \( A_{\text{total}} = 6x + 42 \).

As a product of length and width

Answer:

s:
(a) Light rectangle: \( \boldsymbol{6x} \); Dark rectangle: \( \boldsymbol{42} \)
(b) Sum of two areas: \( \boldsymbol{6x + 42} \); Product of length and width: \( \boldsymbol{6(x + 7)} \) (or \( \boldsymbol{6x + 42} \))