Question

(a) use the calculator to find the perimeter and area of the window. make sure to include the correct units. perimeter: area: (b) a silver wire will be placed around the window. which measure would be used in finding the amount of wire needed? perimeter area (c) the window’s glass will be replaced. which measure would be used in finding the amount of glass needed? perimeter area

Explanation:

Part (a)

Step 1: Recall the formulas for the perimeter and area of a rectangle

For a rectangle with length \( l \) and width \( w \):

• The perimeter \( P \) is given by the formula \( P = 2(l + w) \)
• The area \( A \) is given by the formula \( A = l\times w \)

From the diagram, the length \( l = 64\) in and the width \( w = 34\) in.

Step 2: Calculate the perimeter

Substitute \( l = 64 \) and \( w = 34 \) into the perimeter formula:

$$
LATEXBLOCK0
$$

Step 3: Calculate the area

Substitute \( l = 64 \) and \( w = 34 \) into the area formula:

$$
LATEXBLOCK1
$$

Part (b)

A silver wire placed around the window means we are covering the boundary of the window. The perimeter of a shape is the distance around the boundary of the shape. So, to find the amount of wire needed, we use the perimeter.

Part (c)

To replace the glass in the window, we need to cover the surface of the window. The area of a shape is the amount of space inside the boundary of the shape. So, to find the amount of glass needed, we use the area.

Final Answers:

(a)

• Perimeter: \(\boldsymbol{196}\) in
• Area: \(\boldsymbol{2176}\) in\(^2\)

(b) The measure used to find the amount of wire needed is \(\boldsymbol{\text{Perimeter}}\)

(c) The measure used to find the amount of glass needed is \(\boldsymbol{\text{Area}}\)

Answer:

Part (a)

Step 1: Recall the formulas for the perimeter and area of a rectangle

For a rectangle with length \( l \) and width \( w \):

• The perimeter \( P \) is given by the formula \( P = 2(l + w) \)
• The area \( A \) is given by the formula \( A = l\times w \)

From the diagram, the length \( l = 64\) in and the width \( w = 34\) in.

Step 2: Calculate the perimeter

Substitute \( l = 64 \) and \( w = 34 \) into the perimeter formula:

$$
LATEXBLOCK0
$$

Step 3: Calculate the area

Substitute \( l = 64 \) and \( w = 34 \) into the area formula:

$$
LATEXBLOCK1
$$

Part (b)

A silver wire placed around the window means we are covering the boundary of the window. The perimeter of a shape is the distance around the boundary of the shape. So, to find the amount of wire needed, we use the perimeter.

Part (c)

To replace the glass in the window, we need to cover the surface of the window. The area of a shape is the amount of space inside the boundary of the shape. So, to find the amount of glass needed, we use the area.

Final Answers:

(a)

• Perimeter: \(\boldsymbol{196}\) in
• Area: \(\boldsymbol{2176}\) in\(^2\)

(b) The measure used to find the amount of wire needed is \(\boldsymbol{\text{Perimeter}}\)

(c) The measure used to find the amount of glass needed is \(\boldsymbol{\text{Area}}\)