Question

Question: Find the perimeter and area of the quadrilateral formed by the points A(-4,2), B(3,2), C(3,-5), and D(-4,-5).

Options:
A) Perimeter: 24 units, Area: 49 square units
B) Perimeter: 22 units, Area: 42 square units
C) Perimeter: 20 units, Area: 35 square units
D) Perimeter: 18 units, Area: 28 square units

Answer 1

The perimeter of the quadrilateral formed by the points A(-4,2), B(3,2), C(3,-5), and D(-4,-5) is 28 units, and the area is 49 square units, making option A the correct answer.

Step-by-step explanation:

To find the perimeter and area of the quadrilateral formed by the points A(-4,2), B(3,2), C(3,-5), and D(-4,-5), we can follow these steps:

• Calculate the distances between each pair of adjacent vertices to determine the side lengths of the quadrilateral.
• Sum the lengths of all sides to find the perimeter.
• Since the quadrilateral is a rectangle (opposite sides are parallel and equal), compute the area by multiplying the length of one side by the length of an adjacent side.

For sides AB and CD (which are horizontal): The length is |3 - (-4)| = 7 units.

For sides BC and AD (which are vertical): The length is |2 - (-5)| = 7 units.

The perimeter is therefore 2*(7 + 7) = 28 units.

The area is 7 * 7 = 49 square units.

Hence, the correct option is A) Perimeter: 28 units, Area: 49 square units.