What is the area of a quadrilateral with sides 24 and 40 and a shared angle of 135 degrees ?

Thank you

To find the area of a quadrilateral, we can use the formula for the area of a triangle. Since a quadrilateral can be divided into two triangles, we will calculate the area of each triangle separately, and then sum them.

Let's label the given sides and angles of the quadrilateral:

Side A = 24
Side B = 40
Shared angle C = 135 degrees

To find the area of a triangle, we can use the formula:

Area = 0.5 * side1 * side2 * sin(angle)

Considering the first triangle (Triangle ABC), we can label the sides and angles as follows:

Side AB = Side A = 24
Side BC = Side B = 40
Angle C = Shared angle C = 135 degrees

Using the formula, we have:

Area of Triangle ABC = 0.5 * AB * BC * sin(C)

Now, let's calculate the area of Triangle ABC step by step:

1. Convert the angle from degrees to radians:
Angle C in radians = 135 degrees * (π/180) radians/degree

2. Apply the formula to find the area:
Area of Triangle ABC = 0.5 * 24 * 40 * sin(135 degrees * (π/180))

To calculate sin(135 degrees * (π/180)), we need to use the sine function. However, I can provide the numeric result:

Area of Triangle ABC ≈ 405.8316 square units

Now, since the quadrilateral is composed of two triangles, we need to multiply the calculated area of Triangle ABC by 2 to obtain the total area of the quadrilateral:

Area of Quadrilateral ≈ 2 * 405.8316 ≈ 811.6632 square units

So, the approximate area of the quadrilateral with sides 24 and 40 and a shared angle of 135 degrees is 811.6632 square units.