11.1 areas of rectangles
DESCRIPTION
11.1 Areas of rectangles. Postulates. The area of a square is the square of the length of a side. (A = s 2 ) If two figures are congruent, then they have the same area. s. s. Postulates. The area of a region is the sum of the areas of its non-overlapping parts. D. B. C. A. I. II. - PowerPoint PPT PresentationTRANSCRIPT
11.1 AREAS OF RECTANGLES
Postulates The area of a square is the square of
the length of a side. (A = s2)
If two figures are congruent, then they have the same area.
s
s
Postulates The area of a region is the sum of the
areas of its non-overlapping parts.
I II III
A B C D
EF
GE
Altitude To a base, is any segment perpendicular
to the line containing the base from any point on the opposite side.
Theorem The area of a rectangle equals the
product of its base and height.
A=bh
11.2 Areas of Parallelograms, Triangles, and Rhombuses
Theorem The area of a parallelogram equals the
product of a base and the height to that base. (A=bh)
5
12
45°
12
31
Theorem The area of a triangle equals half the
product of a base and the height to that base ( A = ½ bh)
h99
11
Theorem The area of a rhombus equals half the
product of its diagonals.
431 WE 1-20, 27
11-3 Areas of Trapezoids
Theorem The area of a trapezoid equals half the
product of the height and the sum of the bases.
A = ½ h(B1+B2)
h
B1
h
B2
12
14
17
8
13
11 7
This is not isosceles
11-4 Areas of Regular Polygons
Definitions Center of a regular polygon the center of the
circumscribed circle.
Radius of a regular polygon the distance from the center to a vertex. All radii of a figure are congruent.
Central angle of a regular polygon an angle formed by two radii drawn to consecutive vertices. All central angles are congruent.
Apothem of a regular polygon the perpendicular distance from the center of the polygon to a side.Every apothem of a figure is congruent
Theorem The area of a regular polygon is equal
to half the product of the apothem and the perimeter.
A= ½ aP
Apothems are going to be found using special right triangles, and sine, cosine, tangent functions.
Find the area of a regular pentagon with perimeter of 40 centimeters.
Find the area of a regular octagon with a perimeter of 72 inches.
Find the area of a regular hexagon with apothem of 9.
Find the area of a regular polygon with 11 sides inscribed in a circle with a radius of 12.
WORKSHEET
Hw. Pg. 437 WE 10-14Hw. Pg. 442 CE 2-4, 6-8
WE 2-8 (ev) 13-16