Surface Area of Pyramids Lesson 9.2 7.G.6: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Pyramids Pyramids are named from their base shape Most pyramids we’ve seen are square pyramids but there are plenty of others as well…

Parts of a pyramid A regular pyramid is a pyramid whose base is a regular polygon (all sides equal). The lateral faces are triangles. The height of each triangle is the slant height of the pyramid.

Surface Areas of Pyramids and Cones Regular Pyramid The slant height of a pyramid or cone is measured along its lateral surface. Right cone The base of a regular pyramid is a regular polygon, and the lateral faces are all congruent. In a right cone, a line perpendicular to the base through the vertex passes through the center of the base.

Another look Surface Area of Pyramid = Area of Base + Areas of Lateral Faces

Example 1A: Finding Surface Area using a net

Example 1B: Find the Surface Area of a Pyramid Find the surface area of the figure. SA = B + 1/2 Pl = (2.4 • 2.4) + (9.6)(3) 1 2 = 20.16 ft2

You Try! What is the surface area of a square pyramid with a base side length of 9 cm and a slant height of 7 cm? (Draw a picture, then solve) 207 cm2

Example 2: Finding Surface Area of a Triangular Pyramid

Surface Area of a Composite Solid Composite Solid: A figure that consists of two or more geometric shapes

Surface Area of a Composite Solid When finding the surface area of a composite solid, remember that surface area is only the area of the SURFACES (some parts of figures get covered)

Example 3 – Find the surface area of a composite figure 283.5 cm2

Example 4: Real-Life Application

17 bundles Example 4 extension One bundle of shingles covers 32 square feet. How many bundles should you buy to cover the roof? 17 bundles

You Try! 105.6 ft2

Additional Example: Find the Surface Area of a Cone Find the surface area of each figure to the nearest tenth. Use 3.14 for p. SA = pr2 + prl 18 ft = p(72) + p(7)(18) 7 ft = 175p  549.5 ft2

Homework  p.366 #1-3, 8-16 even, 17-20