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8.7: Rectangle Facts

Difficulty Level: At Grade Created by: CK-12

Rectangle Facts – Apply Measurement Formulas

Teacher Notes

Each problem shows a rectangle separated into four smaller rectangles. The areas for three of the four rectangles are given. Students use the data provided and the formula for the area of a rectangle to figure out the dimensions of each of the three rectangles. Once they have found the dimensions of the three rectangles, they can figure out the dimensions of the fourth rectangle and determine its area.

Solutions:

  1. 20 square inches
  2. 32 square inches
  3. 32 square inches
  4. 6 square inches
  5. 56 square inches
  6. 8 square inches

Rectangle Facts – Apply Measurement Formulas

Rectangle \begin{align*}ABCD\end{align*}ABCD is divided into 4 smaller rectangles.

\begin{align*}& \mathbf{Describe:} && \text{The large rectangle contains} \ 4 \ \text{smaller rectangles. The areas of three of the}\\ &&& \text{rectangles are given.} \ A \ \text{is a square. All dimensions are whole numbers.}\\ \\ & \mathbf{My \ Job:} && \text{Use the given areas. Figure out the area of Rectangle} \ C.\\ \\ & \mathbf{Plan:} && \text{Find common factors of the areas.} \ A \ \text{is a square, so the dimensions can be easily}\\ &&& \text{determined. Figure out the dimensions of Rectangles} \ B \ \text{and} \ D. \ \text{This will give the}\\ &&& \text{dimensions for Rectangle} \ C. \ \text{Use the area formula to figure out the area of}\\ &&& \text{Rectangle} \ C.\\ \\ & \mathbf{Solve:} && A \ \text{is a square, so the dimensions are} \ 4 \ \text{in. by} \ 4 \ \text{in. That means that one of the}\\ &&& \text{dimensions of Rectangle} \ B \ \text{is} \ 4 \ \text{inches. The area is} \ 24 \ \text{square inches, so the other}\\ &&& \text{dimension must be} \ 24 \div 4, \ \text{or} \ 6 \ \text{inches. Likewise, one of the dimensions of}\\ &&& \text{Rectangle} \ D \ \text{is} \ 4, \ \text{so the other is} \ 20 \div 4, \ \text{or} \ 5 \ \text{inches. The dimensions of Rectangle}\\ &&& C \ \text{are} \ 6 \ \text{inches from the shared side with Rectangle} \ B \ \text{and} \ 5 \ \text{inches form the}\\ &&& \text{shared side with Rectangle} \ D. \ \text{The area of} \ C \ \text{is} \ 6 \times 5, \ \text{or} \ 30 \ \text{square inches.}\\ \\ & \mathbf{Check:} && A: 4 \ \text{by} \ 4 \ \text{inches with an area of} \ 16 \ \text{sq in.}\\ &&& B: 4 \ \text{by} \ 6 \ \text{inches with an area of} \ 24 \ \text{sq in.}\\ &&& C: 5 \ \text{by} \ 5 \ \text{inches with an area of} \ 30 \ \text{sq in.}\\ &&& D: 4 \ \text{by} \ 5 \ \text{inches with an area of} \ 20 \ \text{sq in.}\end{align*}

1. Rectangle \begin{align*}EFGH\end{align*} is separated into 4 smaller rectangles.

2. Rectangle \begin{align*}JKLM\end{align*} is separated into 4 smaller rectangles.

3. Rectangle \begin{align*}NPQR\end{align*} is separated into 4 smaller rectangles.

4. Rectangle \begin{align*}EFGH\end{align*} is separated into 4 smaller rectangles.

5. Rectangle \begin{align*}JKLM\end{align*} is separated into 4 smaller rectangles.

6. Rectangle \begin{align*}NPQR\end{align*} is separated into 4 smaller rectangles.

Extra for Experts: Rectangle Facts – Apply Measurement Formulas

1. Rectangle \begin{align*}ABCD\end{align*} is separated into 4 smaller rectangles.

2. Rectangle \begin{align*}EFGH\end{align*} is separated into 4 smaller rectangles.

3. Rectangle \begin{align*}JKLM\end{align*} is separated into 4 smaller rectangles.

4. Rectangle \begin{align*}NPQR\end{align*} is separated into 4 smaller rectangles.

5. Rectangle \begin{align*}STUV\end{align*} is separated into 4 smaller rectangles.

6. Rectangle \begin{align*}WXYZ\end{align*} is separated into 4 smaller rectangles.

Solutions:

  1. 21 square inches
  2. 24 square inches
  3. 15 square inches
  4. 80 square inches
  5. 48 square inches
  6. 108 square inches

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CK.MAT.ENG.SE.1.Algebra-Explorations-K-7.8.7

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