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Unit 8: Applying Formulas Sections: 10-3, 10-5, 10-6, 10-7 11-2, 11-4, 11-5, and 11-6

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Learning Target: I will be able to identify the appropriate formula for a figure and find the area, volume, surface area, or perimeter.

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Area of Parallelograms THEOREM 10.1 – Area of a Rectangle The area of a rectangle is the product of its base and height. THEOREM 10.2 – Area of a Parallelogram The area of a parallelogram is the product of a base and a corresponding height.

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Area of Triangle A triangle is half of a parallelogram. THEOREM 10.3 – Area of a Triangle The area of a triangle is half the product of a base and the corresponding height.

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Area of Trapezoid THEOREM 10.4 – Area of a Trapezoid The area of a trapezoid is half the product of the height and the sum of the bases.

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Area of Rhombus and Kite THEOREM 10.5 – Area of a Rhombus or a Kite The area of a rhombus or kite is half the product of the lengths of the diagonals.

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Regular Polygons radius – the distance from the center to a vertex We can center any regular polygon inside of a circle: Regular polygons: -all sides congruent-all angles congruent-convex apothem – perpendicular distance from the center to a side

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THEOREM 10.6 – Area of a Regular Polygon The area of a regular polygon is half the product of the apothem and the perimeter Areas of Regular Polygons

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Regular decagon:

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Words… Circle: the set of all points equidistant from a given point called the center (name a circle by its center) P radius diameter Central angle – an angle whose vertex is the center of the circle.

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Arcs… Semicircle – an arc that is half the circle Minor arc – smaller than a semicircle Major arc – greater than a semicircle Minor Arc: Defined as the same as the measure of its corresponding central angle. Major Arc: This is 360° minus the degree measure of the minor arc that has the same endpoints as the major arc..

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Arc Length… THEOREM 10.9: Circumference of a Circle The circumference of a circle is times the diameter. THEOREM 10.10: Arc Length

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Area… THEOREM 10.11: Area of a Circle The area of a circle is the product of and the square of the radius. THEOREM 10.12: Area of a Sector of a Circle

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Arc Length… Find the length of each arc shown in red. Leave your answer in terms of.

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Area… Find the area of sector ZOM. Leave your answer in terms of.

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Prisms Prism – A 3-dimensional figure with two congruent, parallel faces, called bases. Lateral Faces – Faces that are not bases

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Surface Area of Prisms THEOREM 11.1 – Surface Area of Prism The surface area of a prism is the sum of the lateral area and the area of the two bases. 4 in. 12 in. Regular Pentagon

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Surface Area of Cylinder THEOREM 11.2 – Surface Area of Cylinder The surface area of a cylinder is the sum of the lateral area and the area of the two bases.

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Volume of Prisms 4 cm 6 cm 12 cm THEOREM 11.6 – Volume of Prism The volume of a prism is the product of the area of a base and the height of the prism. Area of the base times the height.

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Volume of Cylinders THEOREM 11.7 – Volume of Cylinder The volume of a cylinder is the product of the area of the base and the height of the cylinder. Find the volume of the following cylinder in terms of π.

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Pyramids Pyramid – A 3-D figure with one face (the base) that is any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex. Regular Pyramid – Base is a regular polygon. Slant Height ( l ) – The length of an altitude of a lateral face of the pyramid. How are the height and slant height related to the edge of the base of a pyramid???

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Surface Area of Pyramids THEOREM 11.3 – Surface Area of Regular Pyramid The surface area of a regular pyramid is the sum of the lateral area and the area of the base.

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Cones Cone – A 3-D figure with a circular base and a curved lateral surface How are the radius, height, and slant height related???

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Surface Area of Cones THEOREM 11.4 – Surface Area of Cone The surface area of a cone is the sum of the lateral area and the area of the base. Find the surface area of the following cone.

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Volume of Pyramids THEOREM 11.8 – Volume of Pyramid The volume of a pyramid is one third the product of the area of a base and the height of the pyramid. The Pyramid arena in Memphis, TN has a base of area 300,000 ft 2. Its height is 321 ft. What is the volume of the pyramid?

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Volume of Cones THEOREM 11.9 – Volume of Cone The volume of a cone is one third the product of the area of the base and the height of the cone. Find the volume of the following cone in terms of π.

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THEOREM 11.10 – Surface Area of a Sphere The surface area of a sphere is four times the product of pi and the square of the radius of the sphere. Surface Area and Volume of a Sphere THEOREM 11.11– Volume of a Sphere The volume of a sphere is four thirds the product of pi and the cube of the radius of the sphere.

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Four Types of Rigid Motion A rigid motion is the action of taking an object and moving it to a different location without altering its shape or size. 1.Translation (slide) 2.Reflection (about a line or an axis) 3.Dilation (little/big) 4.Rotation (clockwise or counterclockwise)

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