Question

You design a tree house using a coordinate plane in which the coordinates are measured in feet. The vertices of the floor are (-2,-3),
(-2,4), (5,4) and (5,-3). Find the perimeter in yards and the area in square yards of the floor.

Answer 1

Answer:

Perimeter = 28 yards

Area = 49 square yards.

Step-by-step explanation:

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Let as consider the vertices of the floor are A(-2,-3), B(-2,4), C(5,4) and D(5,-3).

Using distance formula, we get

$AB=\sqrt{(-2-(-2))^2+(4-(-3))^2}=\sqrt{(-2+2)^2+(4+3)^2}=\sqrt{0+7}^2=7$

Similarly,

$BC=\sqrt{(5-(-2))^2+(4-4)^2}=7$

$CD=\sqrt{(5-5)^2+(4-(-3))^2}=7$

$AD=\sqrt{(5-(-2))^2+(-3-(-3))^2}=7$

It is conclude that, $AB=BC=CD=AD$.

From the given points it is clear that all sides lie on either vertical or horizontal lines.

Since all sides are equal, and adjacent sides are perpendicular, therefore, the base is a square with edge 7 yards.

Perimeter of square floor is

$P=4a=4(7)=28\text{ yards}$

Area of square floor is

$A=a^2=7^2=49\text{ sq. yards}$

Therefore, the perimeter is 28 yards and the area is 49 square yards.