Discovering Geometry Day 56

8.3 Area Problems

8.4 Areas of Regular

Polygons

§  Daily Openers

§  Check and go over homework

8.3 Area Problems

o  Read the problem! TWICE!

o  Draw and label a picture if appropriate

o  Break multi-step problem into manageable parts

Ex. Drew needs to lay down weed mat in his greenhouse. The greenhouse is 15´×102´.

If the weed mat costs $0.75 per square foot, what is the cost for covering the greenhouse?

Ex. If another store sells weed mat for $2.50 per square yard, which would be the better

deal?

Ex. page 449 problem #4 [Old Book]

Homework – pages 435–437 # 1–9

8.4 Areas of Regular Polygons

polygon – a closed geometric figure in a plane (flat surface), formed by connecting

line segments endpoint to endpoint with each segment intersecting exactly

two others.

regular – all the side lengths are the same length and all the angles are the same measure.

apothem – a ^ segment from the center of the polygon’s circumscribed circle to a side

of the polygon.

#of sides / Name
3 / triangle
4 / quadrilateral
5 / pentagon
6 / hexagon
7 / heptagon
8 / octagon
10 / decagon
12 / dodecagon
Area of a Regular Polygon
A = ½ ·a · P, where a = length of the apothem

P = perimeter of the polygon

Ex. Find the area of a regular pentagon with side length of 12 cm and apothem

of length 10 cm.

Ex. Find the area of a regular octagon with side length of 8.6 in and apothem of

length 9 in.

Ex. Find the area of the regular figure:

Ex. If the area of a regular hexagon is 390 un2 and the length of a side of the

hexagon is 10 units, what is the length of the apothem?

Homework – pages 443–444 # 1–14

Daily Openers – 1. Find the area of a rectangle with d = 17 cm and w = 8 cm.

2. Find the height of a parallelogram with A = 255 m2 and b = 25 m.

3. Find the area of the triangle:

4. Find the area of the trapezoid:

5. Find an expression for the area of a kite with d1 = x2 + 1 cm and d2 = 2x + 9 cm.