what is the area of a parallelogram with sides 10 and 13 that form a 30 degree angle?

Question

please help me this is the last question on my homework and i need to know the answer if i want to pass the test on monday

Answer 1

A = base * height

same formula that is used to find the area of a rectangle.

draw altitude from the vertex. you'll get a right triangle with the hypotenue is 10 and of of the angle is 30

find the altitude.

h = sin(30)10
h = 5

A = 13 * 5
A = 65

Answer 2

In a 30-60-90 triangle the hypotenuse is twice the shorter leg.
So the height of the parallelogram and 10 unit side and part of the 13 unit side form such a triangle. So the height is 10/2 = 5. Thus the area is 5*13 = 65 units^2.

Answer 3

The area is given by a x b x sin theta where a = 10 b = 13 theta = 30 deg

therefore the area is = 130 x .5 = 65 square units.