# LESSON 9.1 - raikemath

LESSON 9.1 Areas of Rectangles and Parallelograms AREA OF A RECTANGLE C-81: The area of a rectangle is given by the formula A=bh. Where b is the length of the base and h is the height.

AREA OF A PARALLELOGRAM C-82: The area of a parallelogram is given by the formula A=bh. Where b is the length of the base and h is the height of the parallelogram.

LESSON 9.2 Areas of Triangles, Trapezoids and Kites AREA OF TRIANGLES C-83: The area of a triangle is given by the formula bh A= . Where b2is the length of the base and h is the

height (altitude) of the triangle. AREA OF TRAPEZOIDS C-84: The area of a trapezoid is given by the (b + b )h A = formula . 2

Where the b's are the length of the bases and h is the height of the trapezoid. 1 2 AREA OF KITES C-85: The area of a kite is given by d1 gd2

the formula A= 2 . Where the d's are the length of the diagonals of the triangle. LESSON 9.4 Areas of Regular Polygons AREA OF REG. POLYGONS

A regular n-gon has "n" sides and "n" congruent triangles in its interior. The formula for area of a regular polygon is derived from theses interior congruent triangles. If you know the area of these triangles will you know the area of the polygon? FORMULA TO FIND AREA

OF A REGULAR POLYGON n= # of sides a = apothem length s = sides length bh A =ng 2 as A =ng 2 nas

A= 2 FORMULA TO FIND AREA OF A REGULAR POLYGON C-86: The area of a regular polygon is given by the formula , where a is the apothem nas A= (height of interior 2triangle), s is the length of

each side, and n is the number of sides the polygon has. Because the length of each side times the aP A= P = sn number of sides is the perimeter, we can 2say and . LESSON 9.5 Areas of Circles

AREA OF A CIRCLE C-87: The area of a circle is given by the formula 2 A =r , where A is the area and r is the radius of the circle. LESSON 9.6

Area of Pieces of Circles SECTOR OF A CIRCLE A sector of a circle is the region between two radii of a circle and the included arc. Formula: Central Angle Area of Sector = 2

360 r AREA OF SECTOR EXAMPLE Find area of sector. Central Angle Area of Sector = 2 360 r

45 x = 2 360 12 1 x = 9 144 144 =x 9 16 = x

SEGMENT OF A CIRCLE A segment of a circle is the region between a chord of a circle and the included arc. Formula: Area of Segment=Area of Sector - Area of Triangle See Example on Next Slide SEGMENT OF A CIRCLE EXAMPLE

Find the area of the segment. 2 90 6g6 6 g 360 2 1 36 =36 4 2 36

= 18 4 =9 18 cm 2 ANNULUS An annulus is the region between two concentric circles. Formula: A = R r 2

2 LESSON 9.7 Surface Area TOTAL SURFACE AREA (TSA) The surface area of a solid is the sum of the areas of all the faces or surfaces that enclose the solid.

The faces include the solid's top and bottom (bases) and its remaining surfaces (lateral surfaces or surfaces). TSA OF A RECTANGULAR PRISM Find the area of the rectangular prism.

TSA =2(4g10) + 2(7g4) + 2(7g10) =80 + 56 + 140 =276 cm 2 TSA OF A CYLINDER Formula: TSA =2(r ) + 2 r gh 2 Example: TSA =2(6 ) + 2(6) g20

=2(36 ) + 240 2 =72 + 240 =312un 2 TSA OF A PYRAMID The height of each triangular face is called the slant height.

The slant height is usually represented by "l" Examp (lowercase L). le: TSA = Base Area + Lateral Surface Area 32g25 =25g25 + 4 2 =625 + 4(400) =625 + 1600

=2225 ft2 TSA OF A CONE Formula: TSA = Area of Base + Lateral Surface Area =r2 + rl Example:

TSA =8 2 + 8 9 =64 + 72 =136cm 2

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