find the side length
Find the apothem length
Find the area
Find the perimeter
Challenge (all worth 500)
100

An equilateral triangle has an area of 110√ ̅3cm2.  Find the length of one side.

Drew

2√ ̅110 cm

100

A regular pentagon has the area of 68ft2 and side lengths of 6 ft.  Find the apothem.

Drew

68/15 feet.

100

Find the area of a square with a perimeter of 24 feet.

Jack

36 feet2.

100

Find the perimeter of an equilateral triangle with an apothem measuring 5√3 inches and an area of 50√3 inches2.

Jack

30 inches

100

What is the best duo in all of music history?

Jack

Jack Lordi and Mr. Baroody

200

An equilateral triangle has an area of 110√3cm2. Find the length of one side.

Jack

2√110 cm.

200

Find the apothem of a regular nonagon with a side length of 10 meters and an area of 270 meters2.

Jack

6 meters.

200

Find the area of an equilateral triangle with a side length of 8 feet.

Jack

16√ 3 ft.2

200

A regular polygon with an area of 32 units squared has an apothem of 4 units.  Find the perimeter of the polygon.

Drew

16 units

200

Find the area of the two unshaded sections formed by a rhombus with sides 6 meters in length and an equilateral triangle with sides of 6 meters with the triangle shaded and inscribed inside the rhombus.

Jack

36-9√3 meters2.

300

Find the side length of a regular pentagon with an apothem of 6√3 feet and an area of 180√3 feet2.

Jack

12 feet.

300

Find the apothem of a regular decagon with an area of 492 in.2 and a side length of 8. 

Jack

12.3 in.

300

Find the area of a regular pentagon with side lengths of 11.6 cm and an apothem measuring 8 cm.

Jack

232 cm.2

300

A regular heptadecagon with an area of 510 ft squared has an apothem of 12ft. Find its perimeter.

Drew


85 ft

300

How many yards2 is the area of an equilateral triangle with a side length of 7√3/4 feet?

Jack

147√3/192 yards2

400

Find the side length of a regular octagon with an apothem measuring 10√3. inches and an area of 240√3 inches2.

Jack

3 inches.

400

Find the apothem of a regular undecagon with sides of 17 feet and an area of 841 feet2.

Jack

1682/841 feet.

400

Find the sum of the areas of a regular pentagon with an apothem of 12 and side length of 12√3 and a regular hexagon with side lengths of 6.

Jack

414√3 units2

400

An equilateral triangle has an area of 120 cm2.  Find its perimeter.

Drew

3√(480*√3) all over 2


400

A shaded square is inscribed in an equilateral triangle with 2 vertices located on one side and 1 vertex on each of the remaining two sides. Find the area of the unshaded region if the square has a length of 4 feet and the apothem of the triangle is 15 feet. (Diagram will be drawn if needed).

Jack

225√3/2 - 16 feet2

500

Find the area of an inscribed regular hexagon where the circle has a radius of 8√ ̅3 in.

Drew

288√ ̅3

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