Question

drag the tiles to the correct locations on the image. not all tiles will be used.

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

what are the perimeter and the area of the square?

the perimeter of the square is millimeters.
the area of the square is square millimeters.

Explanation:

⚡ Using: area formulas for rectangles and squares · 🆕 New: Perimeter of Squares with Radicals
Multiplying side lengths containing square roots to find perimeter and area.

Step 1: Calculate the perimeter

A square has four equal sides. To find the perimeter, multiply the side length by \(4\):

$$ P = 4 \times s $$

Substitute \(s = 4\sqrt{5}\):

$$ P = 4 \times 4\sqrt{5} = 16\sqrt{5}\text{ mm} $$

Step 2: Calculate the area

To find the area of a square, multiply the side length by itself:

$$ A = s^2 $$

Substitute \(s = 4\sqrt{5}\):

$$ A = (4\sqrt{5})^2 = 4^2 \times (\sqrt{5})^2 $$

$$ A = 16 \times 5 = 80\text{ mm}^2 $$

Answer:

• The perimeter of the square is \(16\sqrt{5}\) millimeters.
• The area of the square is \(80\) square millimeters.