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 / Name3 / 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.