Question

This figure is a square, with side lengths as shown.

The figure shows a square side with 4 square roots of 5 millimeters.

What are the perimeter and the area of the square?

Answer 1

To find the perimeter and area of a square, we can use the following formulas:

1. **Area (A)** of a square = side length²
2. **Perimeter (P)** of a square = 4 × side length

Given that the side length of the square is \( 4\sqrt{5} \) mm, we can calculate the area and perimeter as follows:

### Area:
\[
A = (4\sqrt{5})^2 = 16 \cdot 5 = 80 \text{ mm}^2
\]

### Perimeter:
\[
P = 4 \times (4\sqrt{5}) = 16\sqrt{5} \text{ mm}
\]

### Summary:
- Area = \( 80 \) mm²
- Perimeter = \( 16\sqrt{5} \) mm