Find the area of these problems?

Question

1. Find the area of a rhombus with a 45 degree angle and sides of 10 ft.

2. Find the area of an equilateral triangle with a perimeter of 24

Answer 1

1. Angle is 45 deg
So if we draw 2 lines dividing the rhombus into 4 triangles,
We can find the height and width of the triangle.

One triangle will have height 10 sin22.5 and width 10 cos22.5
So 1/2 of rhombus has area 10(sin45) x 10(cos45) = 35.355
So are of rhombus = 70.71 sq ft

2. As perimeter is 24, one side is 8, each angle is 60 deg
Height is 8sin60
Area is then 1/2 base x height = 0.5 x 8 x 8sin60 = 27.71

Answer 2

1. Insufficient data. No solution possible

2. A= 1/4side^2*sqrt(3)
side = 24/3 =8
A = 1/4 *8^2*sqrt(3)
A = 16 sqrt(3)

Answer 3

1. 40 sq units
2. 4 sq units