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Identify the Wrong Area Expression for a Rectangle with Length b+7 and Width a
Mathematics
Grade 7
Question Content
Circle the expression that does not represent the area of the outside shaded rectangle. Write its letter in the corresponding numbered box. The rectangle has length b+7 and width a. Options: H. ab + 7, R. a(b + 7), A. ab + 7a
Correct Answer
H
Detailed Solution Steps
1
Step 1: Calculate the area of the large rectangle using Area = length × width. Here, length = b+7, width = a, so Area = a(b+7).
2
Step 2: Use the distributive property to expand a(b+7), which gives ab+7a.
3
Step 3: Compare with the options. ab+7 does not equal the area of the large rectangle, so this is the incorrect expression.
Knowledge Points Involved
1
Area of a Rectangle
The area of a rectangle is calculated by multiplying its length by its width, expressed as A = l×w. This formula is used to find the total space enclosed by the rectangle's sides.
2
Distributive Property
The distributive property states that a(b+c) = ab+ac. It is used to expand algebraic expressions by distributing the term outside the parentheses to each term inside.
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