Question

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1. the rectangle is made up of two smaller rectangles.

image of a rectangle composed of two smaller rectangles, with the first smaller rectangle labeled p units in length and the second 9 units in length, both with a height of 5 units
a. write an expression to represent the total area of the rectangle in square units as the product of the rectangle’s length and width.
b. write an expression to represent the total area of the rectangle in square units as the sum of the areas of the two smaller rectangles.

1. which expressions represent the area of the shaded rectangle in square units? choose all that apply.

a. ( 3(12) - 3(2) )
b. ( 3(12) - 3(10) )
c. ( 3(10) + 3(2) )
d. ( 3(10) )
e. ( 3(12 - 2) )
f. ( 30 )
g. ( 36 - 6 )
h. ( 30 + 6 )
image of a shaded rectangle with a height of 12 units, a white rectangle at the bottom with a height of 2 units and a width of 3 units, and the total width of the shaded and white rectangles is 3 units

Explanation:

Step1: Find total length of big rectangle

Total length = $p + 9$ units, width = 5 units. Area = length $\times$ width.
<Expression>
$\text{Area} = 5(p + 9)$
</Expression>

Step2: Calculate sum of smaller rectangles

Area of first small rectangle: $5p$, area of second: $5\times9=45$. Sum the two areas.
<Expression>
$\text{Area} = 5p + 45$
</Expression>

Step3: Analyze shaded rectangle area

Shaded height = $12 - 2 = 10$ units, width = 3 units. Calculate area and match equivalent expressions.

• Option A: $3(12)-3(2)=36-6=30$
• Option B: $3(12)-3(10)=36-30=6$ (incorrect)
• Option C: $3(10)+3(2)=30+6=36$ (incorrect)
• Option D: $3(10)=30$
• Option E: $3(12-2)=3\times10=30$
• Option F: $30$
• Option G: $36-6=30$
• Option H: $30+6=36$ (incorrect)

Answer:

1. a. $\boldsymbol{5(p + 9)}$

b. $\boldsymbol{5p + 45}$

1. A. $3(12)-3(2)$, D. $3(10)$, E. $3(12-2)$, F. $30$, G. $36-6$