The size of the obtuse angle of a rhombus is twice the size of its acute angle. The side length of the rhombus is equal to 10 feet. Find its area. Choose the correct choice from the following answers.
A) 90.56 ft.sq	B) 87.5 ft.sq	C) 86.6 ft.sq	D) 75.85 ft.sq	E) 92.52 ft.sq
A rhombus has 2 congruent opposite acute angles and two congruent opposite obtuse angles. One of the properties of a rhombus is that any two internal consecutive angles are supplementary. Let x be the acute angle. The obtuse angle is twice: 2x. Which gives the following equation.   x + 2 x = 180 degrees.   Solve the above equation for x.   3x = 180 degrees.   x = 60 degrees.   We use the formula for the area of a triangle that uses the side lengths and any one of the angles then multiply the area by 2.   area of rhombus = 2 (1 / 2) (10 feet) 2 sin (60 degrees)   = 86.6 feet square (rounded to 1 decimal place)   Answer is 86.6 ft.sq
<result>C</result>
The size of the obtuse angle of a rhombus is twice the size of its acute angle. The side length of the rhombus is equal to 10 feet. Find its area.