Surface Area of Pyramids

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Presentation transcript:

Surface Area of Pyramids

ADDITION TO DIAGRAM – NEW VOCAB The slant height of a regular pyramid is the distance from the vertex to the midpoint of an edge of the base.

The lateral faces of a regular pyramid can be arranged to cover half of a rectangle with a height equal to the slant height of the pyramid. The width of the rectangle is equal to the base perimeter of the pyramid.

Add the surface area formula to the notes for pyramids.

Example 1 Find the surface area of the regular pyramid. n represents the number of sides of the base, and s represents the length of one side of the base, and l is the slant height. n = 3, s = 14, l = 14 Split the base in half and use 30-60-90 triangles to find the height of the base (7√3) SA = .5*14*42+.5*14*7√3 =378.87 square units

Example 2 Find the surface area of the regular pyramid. n represents the number of sides of the base, and s represents the length of one side of the base, and l is the slant height. n = 6, s = 5.2, l = 13 Use 30-60-90 triangles to find the apothem of the base (2.6√3) SA = .5*13*31.2+.5*2.6√3*31.2 =273.05 square units

Example 3 Find the surface area of the regular pyramid. n represents the number of sides of the base, and s represents the length of one side of the base, and l is the slant height. n = 4, s = 12, l = 13 SA = .5*13*48+12*12 =456 square units

Example 4 Work backwards to solve for the missing information. In a rectangular pyramid, one side of the base is 30 in. The slant height of the pyramid is 29 in, and the SA = 4180 square inches. What is the length of the other side of the rectangular base? 4180=.5*29(30*2+2w)+30w 4180=14.5(60+2w)+30w 4180=870+29w+30w 3310=59w 56.1 in =w

Example 5 Work backwards to solve for the missing information. In a triangular pyramid, the base area is 50 square mm. The slant height of the pyramid is 40 mm, and the SA = 250 square mm. What is the perimeter of the triangular base? 250=.5*40*p+50 200=20p 10 mm =p

Example 6 Work backwards to solve for the missing information. In a square pyramid, the slant height is 5 cm, and the SA = 96 square cm. What is the length of one side of the base? 96=.5*5*4s+s^2 96=10s+s^2 0 = s^2+10s-96 Factor to solve for s. 0 = (s+16)(s-6) This gives s = -16 or 6. Since length can’t be negative, s = 6 cm.