LESSON
OBJECTIVES
A = ½ (Perimeter)(apothem)
A = ½ Pa
P = Perimeter of the regular polygon
a = apothem (a segment that is drawn from the center of a regular polygon I to a side of the polygon) EXAMPLES
a) Find the area of a regular pentagon with a perimeter of 40 cm.
STEP 1 Find the value of PQ (apothem)
P
Q
M
STEP 2 Use the formula A = ½ Pa
b) Find the area of a regular hexagon with a perimeter of 42 yards.
STEP 1 Find the value of the apothem
Use the 30­60­90 Δ to find the apothem
STEP 2 Use the formula A = ½ Pa
c) Find the area of a regular nonagon with a perimeter of 108 meters.
STEP 1 Find the value of the apothem
STEP 2 Use the formula A = ½ Pa
EXAMPLES
Find the area of each shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.
Area of the circle
a)
A = πr2
Area of the triangle
A = ½ bh or A = ½Pa
The area of the shaded region is the difference between the area of the circle and the area of the triangle.
b)
Area of the circle
A = πr2
Area of the triangle
A = ½ bh or A = ½Pa
The area of the shaded region is the difference between the area of the circle and the area of the triangle.
c)
Area of the triangle
A = ½ bh or A = ½Pa
Area of the circle
A = πr2
The area of the shaded region is the difference between the area of the triangle and the area of the circle.
HW on LESSON 11­3 p613 14 ­ 22 even
LESSON
OBJECTIVES
a)
Find the area of each figure. Round to the nearest tenth if necessary.
1)
2)
3)
4)
5)
6)
To find the area of an irregular polygon on the coordinate plane, separate the polygon into known figures.
a)
Find the area of each figure. Round to the nearest tenth if necessary.
1)
2)
The vertices of an irregular figure are given. Find the area of each figure. Round to the nearest tenth if necessary.
3) M(­4, 0), N(0, 3), P(5, 3), Q(5, 0)
4) G(­3, ­1), H(­3, 1), I(2, 4), J(5, ­1) K(1, ­3)
HW on LESSON 11­4 p619 8­13 all
LESSON
OBJECTIVES
GEOMETRIC PROBABILITY
­ Probability that involves a geometric measure such as length or area.
Find the probability that a point chosen at random lies in the shaded region.
a)
b)
A SECTOR of a circle is a region of a circle bounded by a central angle and its intercepted arc. a) Find the area of the blue sector.
b) Find the probability that a point chosen at random lies in the blue region.
Find the area of the blue region. Then find the probability that a point chosen at random will be in the blue region.
1)
2)
A regular hexagon is inscribed in a circle with a diameter of 14.
a) Find the area of the red region.
b) Find the probability that a point chosen at random lies in the red region.
HW on LESSON 11­5 p625­p626 7­19 all