Back to all chapters
# Composite Figures

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

As shown in the diagram above, \(ABCDEFGH\) is an inscribed octagon where \(AB=BC=CD=EF=1\) and \(DE=FG=GH=HA=2\).

If the area of the octagon can be expressed as \(a+b\sqrt c,\) where \(a, b, c\) are all integers and \(c\) is square-free, then find the value of \(a+b+c\).

Calculate the area of the shaded region (colored red) in the figure. Give your answer in \( \text{cm}^2 \) to three decimal places.

**Details and Assumptions**:

- You may use the approximation \( \pi = 3.14159 \) and \( \sin^{-1} \left ( \frac 4 5 \right ) = 0.92729 \).

The figure shown is a square with quarter circles drawn from two adjacent corners. Find the ratio of areas \(a: b\).

Give your answer up to 3 decimal places.

×

Problem Loading...

Note Loading...

Set Loading...