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Warm-Up 1) Draw a polygon that is not convex.

Warm-Up 1) Draw a polygon that is not convex. 2) Find the measure of an exterior angle of a regular decagon. 3) Find the circumference and area of a circle with a radius of 4 inches. 4)Find the area of each polygon. Round to the nearest tenth. 2. 3. 2.1 cm. 9. 5. 5.3 cm.

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Warm-Up 1) Draw a polygon that is not convex.

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  1. Warm-Up • 1) Draw a polygon that is not convex. • 2) Find the measure of an exterior angle of a regular decagon. • 3) Find the circumference and area of a circle with a radius of 4 inches. • 4)Find the area of each polygon. Round to the nearest tenth. 2 3 2.1 cm 9 5 5.3 cm

  2. 1) Draw a polygon that is not convex. • 2) Find the measure of an exterior angle of a regular decagon. • Decagon has 10 sides. • 360/10 = 36 degrees • 3) Find the circumference and area of a circle with a radius of 4 inches. A = πr^2 A = π(4)^2 A = 16π A = 50.3 in^2 • C = 2πr • C = 2π(4) • C = 8π • C = 25.1 in

  3. 3)Find the area of each polygon. Round to the nearest tenth. 2 b1 3 2.1 cm 9 5 b2 5.3 cm A = bh A = 5.3(2.1) A = 11.1 cm^2 Area of b1 A = bh A = 2(3) A = 6 Area of b2 A = bh A = 6(7) A = 42 Area of figure A = b1 + b2 A = 6 + 42 A = 48 units^2

  4. Chapter 11 Sections 1 and 3 Exploring Three Dimensional Figures and Surface Area of Prisms and Cylinders

  5. Polyhedron- A closed three-dimensional figure made up of flat polygonal regions. The flat regions formed by the polygons and their interiors are called faces. Pairs of faces intersect in line segments called edges. Points where three or more edges intersect are called vertices.

  6. Prism- A polyhedron with two congruent faces that are polygons contained in parallel planes. Altitude Altitude- The segment perpendicular to the planes containing the two bases. • Regular prism- a prism whose bases are regular polygons. x Cube- a prism in which all the faces are squares. x x

  7. Pyramid- A polyhedron that has all faces except one intersecting at one point. Cylinder- a solid with congruent bases in a pair of parallel planes. Cone- a solid with a circular base and a vertex.

  8. Sphere- A set of all points in space that are a given distance from a given point. Right Prism- A prism whose lateral edges are also altitudes. Oblique Prism- A prism that is not right.

  9. Lateral Area- The area of all the lateral faces of a prism. Lateral area of a Right Prism- If a right prism has a lateral area of L square units, a height of h units, and each base has a perimeter of P units, then L = Ph. Surface Area of a Right Prism- If the total surface area of a right prism is T square units, its height is h units, and each bases has an area of B square units and a perimeter of P units, then T = Ph + 2B.

  10. Axis- The segment whose endpoints are the centers of the circle bases of a cylinder. • Right Cylinder- the axis of a cylinder is also an altitude of the cylinder. • Oblique Cylinder- Not a right cylinder. Axis

  11. Lateral area of a Right Cylinder- If a right cylinder has a lateral area of L square units, a height of h units, and the bases have radii of r units, then L = 2πrh. Surface Area of a Right Cylinder- If the total surface area of a right cylinder is T square units, its height is h units, and the bases have a radii of r units, then T = 2πrh + 2πr2.

  12. Example 3: Find the lateral area of the triangular prism. 7.3 cm 9 cm 10 cm 21 cm 12 cm Perimeter of base P = 10 + 12 + 9 P = 31 cm Area of base B = ½bh B = ½(12)(7.3) B = 43.8 cm^2 Lateral Area L = Ph L = 31(21) L = 651 cm ^2 Surface Area T = Ph + 2B T = 31(21) + 2(43.8) T = 651 + 87.6 T = 738.6 cm^2

  13. Example 4: Find the lateral area of the triangular prism. Lateral Area L = Ph L = 24(20) L = 480 in^2 6 in 8 in 20 in c in Pythagorean Theorem a^2 + b^2 = c^2 8^2 + 6^2 = c^2 64 + 36 = c^2 100 = c^2 10 = c Perimeter of base P = 8 + 6 + 10 P = 24 in Area of base B = ½bh B = ½(6)(8) B = 24 in^2 Surface Area T = Ph + 2B T = 24(20) + 2(24) T = 480 + 48 T = 528 in^2

  14. Example 5: Find the lateral area of the cylinder. Lateral Area L = 2πrh L = 2π(7.1)(4.5) L = 200.7 in^2 7.1 in 4.5 in Surface Area T = 2πrh + 2πr^2 T = 2π(7.1)(4.5) + 2π(7.1)^2 T = 200.7 + 316.7 T = 517.5 in^2

  15. Example 6: Find the lateral area and the surface area of the cylinder. 2.5 in Lateral Area L = 2πrh L = 2π(1.25)(5) L = 39.3 in^2 5 in Surface Area T = 2πrh + 2πr^2 T = 2π(1.25)(5) + 2π(1.25)^2 T = 39.3 + 9.8 T = 49.1 in^2 Find Radius d = 2r 2.5 = 2r 1.25 = r

  16. Example 7) Find the lateral area and the surface area of each right prism. Round to the nearest tenth. 12 cm Lateral Area L = Ph L = 36(10) L 360 cm^2 Surface Area T = Ph + 2B T = 36(10) + 2(60) T = 360 + 120 T = 480 cm^2 9 cm 6 cm 7 cm 10 cm 8 cm Perimeter of Base P = 12 + 9 + 8 + 7 P = 36 cm Area of Base B = ½h(b1 + b2) B = ½(6)(8 + 12) B = 60 cm^2

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