11.1 areas of rectangles

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