BIG idea: Measurement

You can use formulas to find areas of polygons.

Task 1

A real estate company sells plots of land. The plot shown below costs $ 84 , 120 . dollars 84 comma 120 .  What is the price per square foot of the land? Explain how you found your answer.

BIG idea: Measurement

An arc length is a fractional part of the circumference of a circle. The area of a sector is a fractional part of the area of a circle.

Task 2

The stained glass circle-head window has a 2-in. wide frame. The grills divide the semicircular glass pane into four congruent regions.

Image Long Description

1. What is the area of the blue region?
2. What is the outside perimeter of the window frame?

BIG idea: Similarity

The ratio of the perimeters and the ratio of the areas of two similar figures are related to the ratio of the corresponding measures.

Task 3

Regular hexagon ABCDEF has vertices at A ( 4 , 4 3 ) , B ( 8 , 4 3 ) , C ( 10 , 2 3 ) , D ( 8 , 0 ) , eh open 4 comma 4 square root of 3 close comma . b open 8 comma 4 square root of 3 close comma . c open 10 comma 2 square root of 3 close comma d open 8 comma 0 close comma  E(4, 0) and F ( 2 , 2 3 ) . f open 2 comma 2 square root of 3 close .  Suppose the sides of the hexagon are reduced by 40% to produce a similar regular hexagon. What are the perimeter and area of the smaller hexagon rounded to the nearest tenth? Explain how you found your answer.