Question

1. the area of a square is $9\\ cm^2$.

a. how long is each side of the square?
b. what is the perimeter of the square?
refer to the box shown below to answer problems 21 and 22.
*21. this box has how many faces? draw a net to show how the box would look if you cut it apart and flattened it.
*22. if this box is a cube and each edge is 10 inches long, then
a. what is the area of each face?
b. what is the total surface area of the cube?

1. there are 100 centimeters in a meter. how many centimeters equal 2.5 meters?

*24. write the mixed numbers $1\frac{1}{2}$ and $2\frac{1}{2}$ as improper fractions. then multiply the improper fractions and simplify the product.

Explanation:

Problem 20

Step1: Find square side length

Area of square: $A = s^2$, so $s = \sqrt{A}$
$s = \sqrt{9\ \text{cm}^2} = 3\ \text{cm}$

Step2: Calculate square perimeter

Perimeter of square: $P = 4s$
$P = 4 \times 3\ \text{cm} = 12\ \text{cm}$

Problem 21

Step1: Identify cube face count

A cube (box) has 6 flat faces.

Step2: Describe net of cube

A net is 6 connected squares (e.g., 4 in a row with 1 square attached to the top and bottom of one middle square).

Problem 22

Step1: Find face area of cube

Area of 1 face: $A_{\text{face}} = s^2$
$A_{\text{face}} = (10\ \text{in})^2 = 100\ \text{in}^2$

Step2: Calculate total surface area

Total surface area: $SA = 6 \times A_{\text{face}}$
$SA = 6 \times 100\ \text{in}^2 = 600\ \text{in}^2$

Problem 23

Step1: Convert meters to centimeters

Use conversion factor: $1\ \text{m} = 100\ \text{cm}$
$\text{Length} = 2.5\ \text{m} \times 100\ \frac{\text{cm}}{\text{m}} = 250\ \text{cm}$

Problem 24

Step1: Convert mixed to improper fractions

$1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$; $2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$

Step2: Multiply and simplify fractions

$\frac{3}{2} \times \frac{5}{2} = \frac{15}{4} = 3\frac{3}{4}$

Answer:

1. a. $3\ \text{cm}$

b. $12\ \text{cm}$

1. a. 6 faces

b. A net of 6 connected squares (e.g., 4 in a horizontal row, with 1 square attached to the top and bottom of the second square in the row)

1. a. $100\ \text{in}^2$

b. $600\ \text{in}^2$

1. $250\ \text{cm}$
2. Improper fractions: $\frac{3}{2}$ and $\frac{5}{2}$; Simplified product: $\frac{15}{4}$ or $3\frac{3}{4}$