LESSON 9.1Areas of Rectangles and Parallelograms

AREA OF A RECTANGLEC-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 PARALLELOGRAMC-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 9.2Areas of Triangles, Trapezoids and Kites

AREA OF TRIANGLESC-83: The area of a triangle is given by the formula . Where b is the length of the base and h is the height (altitude) of the triangle.

AREA OF TRAPEZOIDSC-84: The area of a trapezoid is given by the formula . Where the b's are the length of the bases and h is the height of the trapezoid.

AREA OF KITESC-85: The area of a kite is given by the formula . Where the d's are the length of the diagonals of the triangle.

LESSON 9.4Areas of Regular Polygons

AREA OF REG. POLYGONSA 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 POLYGONn= # of sidesa = apothem lengths = sides length

FORMULA TO FIND AREA OF A REGULAR POLYGONC-86: The area of a regular polygon is given by the formula , where a is the apothem (height of interior triangle), 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 number of sides is the perimeter, we can say and .

LESSON 9.5Areas of Circles

AREA OF A CIRCLEC-87: The area of a circle is given by the formula , where A is the area and r is the radius of the circle.

LESSON 9.6Area of Pieces of Circles

SECTOR OF A CIRCLEA sector of a circle is the region between two radii of a circle and the included arc.Formula:

AREA OF SECTOR EXAMPLEFind area of sector.

SEGMENT OF A CIRCLEA segment of a circle is the region between a chord of a circle and the included arc.Formula:

SEGMENT OF A CIRCLE EXAMPLEFind the area of the segment.

ANNULUSAn annulus is the region between two concentric circles.Formula:

LESSON 9.7Surface 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 PRISMFind the area of the rectangular prism.

TSA OF A CYLINDERFormula:

Example:

TSA OF A PYRAMID The height of each triangular face is called the slant height.The slant height is usually represented by "l" (lowercase L).Example:

TSA OF A CONEFormula:

Example:

Show how each interior triangle is congruent by SSS and that the apothem is also the height of each interior triangle.See post it Will have to write in formula : A=(asn)/2.

san=p or A=(1/2)apMake the connection that the formula for area of a sector is very similar to that of arc length.Area of the sector - area of triangle

Before you reveal formula make not that the shaded part is made up of two circles with two different radii.Point out that not all solids have two bases such as a cone or pyramid.2(pi r^2) + h pi dMake not that the slant height and the side of the base are always perpendicular making the slant height the altitude of the triangle.

Need to know slant height and side length of base to determine tsaTsa= pi r l + pi r^2