Question

Look at the two figures below. The rectangle is 8x2, and the square is 4x4. Which figure looks like it has the larger area?Which looks like it has the larger perimeter?Now calculate the area and perimeter of each figure.Which has the larger area?Which has the larger perimeter?

Answer 1

Let's calculate the area and the perimeter of each one.

First, the rectangle 2x8.

The area of a triangle is just the multiplication of the two different sizes of it. In the present case, one is 2 and the other is 8. From this, we are able to calculate as follows:

`\begin{gathered} A_{\text{rec}}=2*8 \\ A_{\text{rec}}=16 \end{gathered}`

To calculate the perimeter, we will sum the length of each one of the sides. Because the rectangle has 2 sides with length 2, and the other 2 have length 8, we have the following calculation for the perimeter:

`\begin{gathered} P_{\text{rec}}=2+2+8+8 \\ P_{\text{rec}}=20 \end{gathered}`

Now, we are able to do the same for the square.

The area of a square is equal to the square of its side. From this, we can calculate it as follows:

`\begin{gathered} A_{\text{sqr}}=4^2 \\ A_{\text{sqr}}=4*4 \\ A_{\text{sqr}}=16 \end{gathered}`

Now, to calculate the perimeter of the square, because each of the sides has the same length, we calculate as follows:

`\begin{gathered} P_{\text{sqr}}=4+4+4+4 \\ P_(sqr)=16 \end{gathered}`

From the above-developed solution, we are able to answer the questions, concluding that both figures have the same area and the rectangle has a larger perimeter.