Question

The vertices of a y rectangle are 8 A(1,7), B (3,7). C(3, 1.5), and 6 D (1, 1.5). Find the perimeter and the area of 3 the rectangle.

Answer 1

Let us first find the measures of the sides.

Width

We can find the width calculating the distance between points A and B. Doing so, we have:

The distance on the y-axis is 0 as they have the same coordinate

The distance on the x-axis is 2 ( x2 - x1= 3 - 1 = 2)

So, the width of the rectangle is 2.

Length

We can find the length calculating the distance between points B and C. Doing so, we have:

The distance on the x-axis is 0 as they have the same coordinate

The distance on the y-axis is 5.5 ( y2 - y1= 7 - 1.5 = 5.5)

So, the length of the rectangle is 5.5.

Using the formula for the perimeter, we have:

P= 2L + 2W (P:perimeter, l: length, w:width)

P= 2*(5.5) + 2*(2) (Replacing)

P= 11 + 4 (Multiplying)

P=15 (Adding)

The perimeter is 15

Using the formula for the area, we have:

A=l*w (A:area, l: length, w:width)

A=(2)*(5.5) (Replacing)

A= 11 (Multiplying)

The area is 11