Question

Rectangle STUV with vertices: S(-3,-1), T(1,-4), U(7,4), V(3,7). What is the perimeter and area?

a) Perimeter: 24 units, Area: 26 square units
b) Perimeter: 26 units, Area: 24 square units
c) Perimeter: 20 units, Area: 22 square units
d) Perimeter: 22 units, Area: 20 square units

Answer 1

The perimeter of the rectangle is 35 units and the area is 50 square units.

Step-by-step explanation:

To find the perimeter of the rectangle, we need to find the lengths of all four sides and add them together. Using the distance formula, we can calculate the length of each side:

1. Side ST = √((-3-1)^2 + (-1-(-4))^2) = 5
2. Side TU = √((1-7)^2 + (-4-4)^2) = 10
3. Side UV = √((7-3)^2 + (4-7)^2) = 5
4. Side VS = √((3+3)^2 + (7-(-1))^2) = 15

Therefore, the perimeter is 5 + 10 + 5 + 15 = 35 units.

To find the area of the rectangle, we can use the formula:

Area = length × width

Using the distance formula, we can calculate the length and width as follows:

Length = √((-3-1)^2 + (-1-(-4))^2) = 5

Width = √((1-7)^2 + (-4-4)^2) = 10

Therefore, the area is 5 × 10 = 50 square units.