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Composite Figures

Overlap, inscribe, and circumscribe a collection of simple geometric shapes to make a complex, composite figure. See more

Composite Figures

         

If \(ACDE \) is a rectangle and \(B\) is a point on side \(AC\) such that \( \triangle BED\) is an equilateral triangle with side length \(36,\) 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 \( a \sqrt{b} + c \pi \), where \(a, b,\) and \(c \) are integers and \(b\) is not divisible by the square of a prime. What is the value of \(a+b+c\)?

If the side length of a regular octagon is \(8\), what is the area of the octagon?

If the side length of a regular hexagon is \(6\), what is the area of the hexagon?

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

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