Question

Find the perimeter and the area of ABCD with vertices A(3, 5), B(6, 5), C(4, -1), and D(1, -1). Round your answer to the nearest hundredth place, if necessary.

Perimeter:___ units
Area:___units​

Answer 1

The perimeter is 19.28 units. The area of the quadrilateral ABCD is 18 square units.

Step-by-step explanation:

The perimeter of a polygon is the sum of the lengths of its sides. To find the perimeter of the quadrilateral ABCD, we need to find the lengths of the four sides AB, BC, CD, and DA, and then add them together.

Using the distance formula, we can find the lengths of the sides:

AB = sqrt((6-3)^2 + (5-5)^2) = 3

BC = sqrt((4-6)^2 + (-1-5)^2) = 7.28

CD = sqrt((1-4)^2 + (-1--1)^2) = 3

DA = sqrt((3-1)^2 + (5--1)^2) = 6

Now, we can find the perimeter by adding up the lengths of the sides:

Perimeter = AB + BC + CD + DA = 3 + 7.28 + 3 + 6 = 19.28 units

Computing the area of a quadrilateral requires knowledge of its shape. The most general way to compute the area of an arbitrary quadrilateral is to decompose it into triangles and compute each triangle's area. However, for a special type of quadrilateral called a trapezoid, we can use a simpler formula:

Area = (sum of the lengths of the parallel sides) * (distance between the parallel sides) / 2

In this case, we can see that AB and CD are parallel sides, and the distance between them is 6. Therefore, we can compute the area as:

Area = (AB + CD) * 6 / 2 = 6 * 6 / 2 = 18 square units