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1. Interior angle of a regular pentagon ●○○○○ 10 ptsFind the measure, in degrees, of an interior angle of a regular pentagon.
2. Volume of a regular pentagonal prism ●○○○○ 10 ptsA right prism has regular pentagons as its bases. The side length of each pentagonal base is 4 cm and the height of the prism is 11 cm. Find the volume of the prism in cubic cm. Use the area of a regular pentagon $\approx 1.720477\,s^2$ for side length $s$. Round to two decimal places.
3. Total surface area of a pentagonal prism ●○○○○ 10 ptsA regular pentagonal prism has a base side length of 6 centimeters, a base apothem of 4 centimeters, and a height of 5 centimeters. Find its total surface area in square centimeters.
4. Side length from heptagon area ●○○○○ 10 ptsA regular heptagon has area $78.105$ square cm. Find its side length in cm, using the area formula $A \approx 3.633912444\,x^2$, where $x$ is the side length. Round to three decimal places.
5. Angle in a regular pentagon ●●○○○ 20 ptsIn a regular pentagon $PQRST$, find the measure of $\angle PRS$ in degrees.
6. Angle in pentagon with inner triangle ●●○○○ 20 ptsIn a regular pentagon $ABCDE$, an equilateral triangle $ABM$ is drawn so that $M$ lies inside the pentagon. Determine the size of the angle $BCM$ in degrees.
7. Area of a regular pentagon from perimeter ●●○○○ 20 ptsA regular pentagon has perimeter $85$ cm. Find its area in square centimetres. Round to the nearest square centimetre.
8. Apothem of a regular pentagon ●●○○○ 20 ptsA regular pentagon has sides of length 4 m. Find the length of its apothem, in metres. Round to two decimal places.
9. Angle in a pentagon with interior point ●●●●○ 100 ptsLet $P$ be a point inside regular pentagon $ABCDE$ such that $\angle PAB=48^{\circ}$ and $\angle PDC=42^{\circ}$. Find $\angle BPC$, in degrees.
10. Cosine squared in a heptagon ●●●●○ 100 ptsLet $ABCDEFG$ be a regular heptagon with center $O$. Let $M$ be the centroid of triangle $ABD$. Find $\cos^2 \angle GOM$. Give your answer as a decimal.

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