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 area of rectangle formula

The area of a rectangle is given by \( A = \text{length} \times \text{width} \). For the light rectangle, length is 3 and width is 5.
\( A_{\text{light}} = 3 \times 5 \)

Step2: Calculate the product

\( 3 \times 5 = 15 \)

Dark Rectangle (Bottom)

Step1: Recall area of rectangle formula

The area of a rectangle is \( A = \text{length} \times \text{width} \). For the dark rectangle, length is 3 and width is \( x \).
\( A_{\text{dark}} = 3 \times x \)

Step2: Simplify the expression

\( 3 \times x = 3x \)

Part (b)

As a sum of two areas

Step1: Add the areas of the two rectangles

We know the area of the light rectangle is 15 and the dark one is \( 3x \). So the total area \( A_{\text{total}} = 15 + 3x \)

As a product of length and width

Answer:

s:
(a) Light rectangle: \(\boldsymbol{15}\); Dark rectangle: \(\boldsymbol{3x}\)
(b) Sum of two areas: \(\boldsymbol{15 + 3x}\); Product of length and width: \(\boldsymbol{3(5 + x)}\) (or \(\boldsymbol{15 + 3x}\) after expansion)