The surface area of a trianglular pyramid is 305 square inches. the area of the base is 35 square inches. Each face has a base of 9 inches. What is the slant height?

Subtract 35 from 305, and you get 270. The formula for the area of a triangle, where b is base and h is height, is b * h / 2. There are three faces, or 3 triangles, and we know the base, so we can say that 3 * 9 * h / 2 = 270 => 27 * h / 2 = 270 => 27 * h / 2 * 2 = 270 * 2 => 27 * h = 540 => 27 * h / 27 = 540 / 27 => h = 20, so the slant height is 20 inches.

305 = 35 + 3 * [( 9 * s) / 2] ; where s = the slant height ;

270 = 3 * [( 9 * s) / 2] ;

90 = ( 9 * s ) / 2 ;

180 = 9 * s ;

s = 20 inches.

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