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

To find the area of a quadrilateral with given side lengths and an included angle, you can use the formula:

Area = (1/2) * a * b * sin(C)

where:
- a and b are the lengths of the two sides adjacent to the included angle, in this case, 24 and 40.
- C is the included angle, in this case, 135 degrees.
- sin(C) is the sine of the included angle.

So, let's calculate the area using this formula:

Step 1: Convert the angle from degrees to radians.
To use the sine function, we need to convert the angle from degrees to radians. The conversion formula is: radians = degrees * π / 180. So, for 135 degrees:

C (in radians) = 135 * π / 180

Step 2: Calculate the sine of the angle.
Use a calculator to find the value of sin(C).

sin(C) ≈ sin(135 * π / 180)

Step 3: Calculate the area.
Now, substitute the values into the formula:

Area = (1/2) * a * b * sin(C)
Area = (1/2) * 24 * 40 * sin(C)

Substituting the value of sin(C) will give the final answer.