Question

ciera is creating a logo the figure on the grid shows the background determine the ration of the area of the inner square to the area of the outer square SUMMARY:the area of the inner square is: the area of the outer square:the ratio of the area of the inner square to the area of the outer square is:

Answer 1

1 : The area of the inner square is 52 square units. The area of the outer square is 100 square units.

2: The ratio of the area of the inner square to the area of the outer square is 0.52

Explanation:

Answer 2

Given that Ciera is creating a logo on the figure grid, let's find the area of inner square to the area of the outter square.

• Area of inner square:

Let's first find the length of one side of the inner square.

Take two end points:

(x1, y1) ==> (0, 4)

(x2, y2) ==> (4, 10)

Apply the distance formula:

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ \\ d=√((4-0)^2+(10-4)^2) \\ \\ d=√(4^2+6^2) \\ \\ d=√(16+36) \\ \\ d=√(52) \\ \\ d=7.2\text{ units} \end{gathered}`

The length of one side of the inner square is 7.2 units.

To find the area, apply the formula:

`A=l^2`

Where:

l = 7.2 units

We have:

`Area=7.2^2=52\text{ square units}`

Therefore, the area of the inner square is 52 square units.

• Area of the outer square:

From the graph, the length of one side of the outer square is:

L = 10 units.

The area will be:

`A=10^2=100\text{ square units}`

The area of the outer square is 100 square units.

• Ratio of area of inner square to area of outer square:

For the ratio, we have:

`\begin{gathered} Ratio=Area\text{ of inner square : Area of outer square} \\ \\ Ratio=52:100 \\ \\ Ratio=13:25 \end{gathered}`

Therefore, the ratio of the area inner square to the area of the outer square is 13 : 25

ANSWER:

The area of the inner square is: 52 square units

The area of the outer square is: 100 square units

The ratio of the area of the inner square to the area of the outer square is: 13 : 25