Geometry

Composite Figures

Composite Figures - Solving with Algebra

         

If ACDEACDE is a rectangle and BB is a point on side ACAC such that BED \triangle BED is an equilateral triangle with side length 36,36, what is the area of the shaded region in the above diagram?

On each of the edges of an equilateral triangle with side length 28, we construct a semicircle with diameter 28 that extends outwards. The area of the enclosed figure has the form ab+cπ a \sqrt{b} + c \pi , where a,b,a, b, and cc are integers and bb is not divisible by the square of a prime. What is the value of a+b+ca+b+c?

If the side length of a regular octagon is 88, what is the area of the octagon?

If the side length of a regular hexagon is 66, what is the area of the hexagon?

What is the area of an annulus with inner radius 3 3 and outer radius 8?8?

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