SOLUTION: You have a quadrilateral with sides measuring 7cm, 8cm, 10cm, and 11cm, and the angle between the two shortest sides is 75°. Calculate the area of the quadrilateral.

Algebra ->  Formulas -> SOLUTION: You have a quadrilateral with sides measuring 7cm, 8cm, 10cm, and 11cm, and the angle between the two shortest sides is 75°. Calculate the area of the quadrilateral.      Log On


   

Question 1203065: You have a quadrilateral with sides measuring 7cm, 8cm, 10cm, and 11cm, and the angle between the two shortest sides is 75°. Calculate the area of the quadrilateral.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

(0)  Draw the diagonal in the quadrilateral, opposite to the angle of 75°.



(1)  Using the cosine law, calculate the length of this diagonal.



(2)  Calculate the area "area_1" of the smaller triangle using the formula

         area_1 = %281%2F2%29%2A7%2A8%2Asin%2875%5Eo%29  (half-product of two side lengths by sine of the angle between these sides).



(3)  Calculate the area "area_2" of the larger triangle using the Heron's formula.



(4)  Now the answer is this sum

         area of the quadrilateral = area_1 + area_2.


Having these instructions, complete the solution on your own.