Composite Figures - Solving with Algebra Practice Problems Online

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?

{329}\sqrt{2}

{339}

{334}

{324}\sqrt{3}

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?

128

128\sqrt{2}

128+128\sqrt{2}

196+128\sqrt{2}

If the side length of a regular hexagon is $6$ , what is the area of the hexagon?

27\sqrt{6}

36\sqrt{6}

45\sqrt{3}

54\sqrt{3}

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

{58}\pi

{64}\pi

{55}\pi

{61}\pi

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Composite Figures - Solving with Algebra

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Composite Figures - Solving with Algebra