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**3.2a: Surface Area of Prisms and Cylinders**

Primary M(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures (including composite figures) or surface area or volume of three Secondary M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem)

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**Prism: a 3-D solid with 1) 2 bases – which are parallel and congruent **

3-D figures- Solid figures. When the sides are polygons, its called a polyhedron. Prism: a 3-D solid with 1) 2 bases – which are parallel and congruent 2) lateral faces that are parallelograms * names by the shape of their bases Base Lateral Edge Altitude (height)- Distance between the bases Base (parallel & Congruent) Lateral Face – parallel sides not the base

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Areas of the Solids Lateral Area (LA) – the sum of the areas of the lateral faces only. Does not include the area of the bases. Surface Area (SA) – the sum of the areas of ALL the faces. Lateral area + area of the bases

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**Lateral Area of a Right Prism**

P = Perimeter of the base h= height between the bases (altitude) Surface Area of a Right Prism B = Area of one Base

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**Ex: Find the lateral & surface areas of the triangular prism.**

LA = Ph P = 6*3 = 18 LA = 18*10 LA = 180 in2 S = 2B + Ph S = 2(15.59) + 180 S = S = in2 6 in. 60o 10 in.

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Find the Surface Area

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**Find the lateral and surface area**

Of the regular pentagonal prism 10 ft

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**Cylinders: 1) has 2 circular bases**

2) bases are both parallel and congruent Oblique Cylinder- The axis is longer than the altitude Right cylinder – the axis is the same as the altitude altitude axis

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**Lateral Area of a Right Prism**

C = circumference of the base circle h= height between the bases (altitude) Surface Area of a Right Prism B = Area of one Base

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**Find the surface area and lateral area**

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**A right cylinder has a surface area of 400 square mm. **

Example A right cylinder has a surface area of 400 square mm. Find the height of the cylinder if the diameter of the base of the cylinder is 10 mm.

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example2 If the side of a cube is doubled, what happens to the surface area ?

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**The Lateral Area of a right rectangular prism is 784 square cm. **

Challenge The Lateral Area of a right rectangular prism is 784 square cm. Its length is three times its width. Its height is twice its width. Find the surface area.

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**Ex. 1 – Released Item from 2007 NECAP**

A square with a side length of 8.0 cm is rolled up, without overlap, to form the lateral surface of a cylinder. What is the radius of the cylinder to the nearest tenth of a centimeter? Ex 2. Find the Surface Area 13 in 4 in 12 in 5 in

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Homework

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