SWBAT: Find the area of an equilateral triangle and other regular polygons

 Make a circle and cut it out.  Draw four diameters, equally spaced.  Cut the circle apart along these diagonals.  What new shapes do you have? Pizza!  How many are there and how do they compare?  Put them together alternately pointing the slices  What new shape does this resemble? A parallelogram!

area of a parallelogram base of the “parallelogram” is half the circumference of the circle height of the “parallelogram” is the radius of the circle simplify using algebra VOILA… the area of a circle!

SStart with a regular hexagon DDraw three diagonals that connect opposite vertices. WWhat kind of shapes are created? HHow many? HHow do they compare to each other? SSo, let’s find the area of one triangle and multiply it by six!

6b is the perimeter! apothem: the distance between the center and a side of a regular polygon. The area of any regular polygon is half the apothem times the perimeter.

1) a regular hexagon with 4 inch sides. First, determine the angle at the top of the triangles (The altitude bisects that angle). Then, find the length of the apothem, using a special right triangle, or trig functions. (The altitude bisects the base of the triangles.)

2) a regular octagon with 7 foot sides.

3) a regular pentagon with an apothem of 8

4) 8

5)6)7) AB C 4 must use 30°-60°-90° must use 45°-45°-90° must use trig!

 define apothem  Day 1 – ex  Day 2 – ex. 14 – 34 even, 35, 42, 43, 50, 51

The sides are congruent The height is also the altitude. This creates two 30°-60°-90° triangles. Find the height: And the area is ss s h

Find the area of an equilateral triangle with a side of 10.