Question

Pentagons N And P are similar.

The area of N is 19cm².
Calculate the area of P.
N 5cm And 3 cm
P 40cm And 15 cm
​

Answer 1

HOPE THIS HELPS!!

Step-by-step explanation:

If pentagons N and P are similar, it means that they have the same shape but possibly different sizes. When two polygons are similar, their corresponding sides are proportional.

Given the information provided, we know the following:

- The area of pentagon N is 19 cm².

- The sides of pentagon N are 5 cm and 3 cm.

- The sides of pentagon P are 40 cm and 15 cm.

To find the area of pentagon P, we can use the concept of similarity and ratios.

First, we calculate the ratio of the sides between N and P. Let's take the longer side lengths:

Ratio = (Side length of P) / (Side length of N)

= 40 cm / 5 cm

= 8

This means that the corresponding sides of pentagon P are 8 times larger than those of pentagon N.

Next, we calculate the ratio of the areas between N and P. Since area is a 2-dimensional measurement, the ratio is the square of the side ratio:

Area ratio = (Ratio of side lengths)²

= 8²

= 64

Therefore, the area of pentagon P is 19 cm² multiplied by the area ratio:

Area of P = Area of N x Area ratio

= 19 cm² x 64

= 1216 cm²

Thus, the area of pentagon P is 1216 cm².

Answer 2

To calculate the area of pentagon P, use the concept of similarity and set up a ratio between the side lengths and areas of the two pentagons. Plug in the given numbers and solve for P's area.

Step-by-step explanation:

To calculate the area of pentagon P, we can use the concept of similarity. Since pentagons N and P are similar, their corresponding sides are in proportion. We can set up the following ratio:

N's side length / P's side length = N's area / P's area

Plugging in the given numbers, we get:

5 / 3 = 19 / P's area

Solving for P's area:

P's area = (3 * 19) / 5 = 11.4 cm²