Question

Question 5

The four sequential sides of a quadrilateral have lengths a = 5.3, b= 8.9, c= 10.2, and d = 11.3 (all
measured in yards). The angle between the two smallest sides is a = 102.
What is the area of this figure?
area =

Answer 1

hope help you keep smiling a =7.35*3.44

Answer 2

To find the area of this quadrilateral, we need to first find its height, which requires finding the length of one of its sides.

Since the angle between the two smallest sides (a and b) is given as 102 degrees, we can use the Law of Cosines to find the length of the side between them:

c^2 = a^2 + b^2 - 2ab * cos(102)

c = sqrt(a^2 + b^2 - 2ab * cos(102))

Substituting the values for a, b, and the cosine of 102 degrees, we get:

c = sqrt(5.3^2 + 8.9^2 - 2 * 5.3 * 8.9 * cos(102))
c = sqrt(28.49 + 78.81 - 95.47)
c = sqrt(11.83)
c ≈ 3.44

So, the length of the side between a and b is approximately 3.44 yards.

Next, we need to find the height of the quadrilateral, which is perpendicular to side c and bisects it. The height is given by:

h = (b * sin(102)) / sin(c/2)

We can use the sine of 102 degrees and the value of c we found above to calculate h:

h = (8.9 * sin(102)) / sin(3.44/2)
h ≈ 7.35

Finally, to find the area of the quadrilateral, we multiply the height by the length of c:

A = h * c
A ≈ 7.35 * 3.44
A ≈ 25.3

So, the area of the quadrilateral is approximately 25.3 square yards