Surface area of a square pyramidIt is not complicated to derive the formula of the surface area of a square pyramid. The word slant refers also to something that is oblique or bent, or something that is not vertical or straight up. Basically, anything that is not horizontal or vertical! The area of the square is s^{2} The area of one triangle is (s × l)/2 Since there are 4 triangles, the area is 4 × (s × l)/2 = 2 × s × l Therefore, the surface area, call it SA is: SA = s^{2} + 2 × s × l : Example #1: Find the surface area of a square pyramid with a base length of 5 cm, and a slant height of 10 cm SA = s^{2} + 2 × s × l SA = 5^{2} + 2 × 5 × 10 SA = 25 + 100 SA = 125 cm^{2} Example #2: Find the surface area with a base length of 3 cm, and a slant height of 2 cm SA = s^{2} + 2 × s × l SA = 3^{2} + 2 × 3 × 2 SA = 9 + 12 SA = 21 cm^{2} Example #3: Find the surface area with a base length of 1/2 cm, and a slant height of 1/4 cm SA = s^{2} + 2 × s × l SA = (1/2)^{2} + 2 × 1/2 × 1/4 SA = 1/4 + 1 × 1/4 SA = 1/4 + 1/4 SA = 2/4 SA = 1/2 cm^{2} 




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