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Word Problems
100
Definition: a line from the center of a regular polygon at right angles to any of its sides. What is it?
An apothem
100
What is the formula for a regular polygon?
(nsa)÷2
100
What is the side length of a pentagon with an area of 81cm² and an apothem length of 6cm?
5.4cm
100
A backyard hockey rink in the shape of a regular hexagon has an apothem of 12m and an area of 200m². What is the rinks side lengths?
The rinks side lengths ≈5.56m
200
What makes a polygon regular?
If it has congruent sides and has congruent interior angles.
200
What is the area of a regular hexagon with a side length of 4cm and an apothem of 3cm?
36cm²
200
What is the apothem length of a octagon with an area of 160dm² and a side length of 5dm?
8dm
200
Mrs.Clarker wants to put a swimming pool in her backyard to enjoy during the summer with her kids. She wants it to have an area of 225m², side lengths of 3m and an apothem of 15m but she isn't sure what shape to tell the builders to make it. What shape is Mrs.Clarker's pool going to have to be?
Mrs.Clarker's pool is going to be a decagon.
300
There are four types of polygons. What are they?
Regular, Irregular, Concave, Complex
300
What is the area of a regular decagon with a side length of 6.7cm and an apothem length of 2.5cm?
83.75cm²
300
What shape has an interior angle of 144°?
A decagon
300
Jackson, Tristan and Tyler are doing an art project for school. They have to completely fill in a huge board with drawings on it. The drawing board is in the shape of a dodecagon. Before they start they want to figure out how much work it is going to be to fill in the whole board with drawings so they decide to calculate the area of it. First they measure one side of the drawing board and it measures 15.7cm. Then they measure the apothem of the drawing boards which they figure out is 25.8cm. What is the area of the drawing board that the boys have to draw on?
The drawing boards area is 2,430.36cm².
400
What is a hendecagon?
A hendecagon is a polygon with 11 sides.
400
What is the area of a nonagon with a side length of 3dam and an apothem length of 3200cm?
43.2dam² or 43, 200, 000cm²
400
What is the interior angle of a hendecagon?
147.273°
400
A craftsperson creates a pattern with tiles in the shape of a regular hexagon whose sides measure 20cm. Given that the apothem of each hexagonal tile is 8.7cm, how many tiles will the craftsperson have to install for that total area of the pattern to be 51 678cm²?
99 tiles are needed.
500
Polygon is a greek word. Poly means ... Gon means ... Together that means ...
Poly: many Gon: angle Polygon: many angle
500
What is the area of a dodecagon with a side length of 0.402hm and an apothem length of 0.973m?
≈0.023hm² or ≈234.69m²
500
How many sides does a shape with an area of 432.096hm², an apothem length 12.86hm of and a side length 9.6hm of have?
7 or a heptagon
500
Tom wants to know the area of his swimming pool which is shaped like a regular heptadecagon and a regular tridecagon and an equilateral triangle that are attached. Their side lengths are all equal to 5m. The heptadecagon's apothem is 1.5dam, the tridecagon's apothem is 12500mm, and the triangle's height is 4.78m. What is the area of the pool in meters?
Heptadecagon= 637.5m Tridecagon= 406.25m Triangle=35.85m Total=1079.6m