This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
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janetolabanji44, let's knock this out. Step 1: Identify the given information. The height of the pyramid (h) is 8 cm. The side length of the square base (s) is 6 cm. Step 2: Calculate the area of the square base. Area of base = s^2 Area of base = 6^2 cm^2 Area of base = 36 cm^2 Step 3: Calculate the slant height (l) of the pyramid. The slant height can be found using the Pythagorean theorem, considering the height of the pyramid, half the base side length, and the slant height as a right triangle. l = sqrt(h^2 + ((s)/(2))^2) l = sqrt(8^2 + ((6)/(2))^2) l = sqrt(8^2 + 3^2) l = sqrt(64 + 9) l = sqrt(73) cm Step 4: Calculate the area of one triangular face. The area of a triangle is (1)/(2) × base × height. In this case, the base of the triangle is the side of the square base (s), and the height of the triangle is the slant height (l). Area of one triangular face = (1)/(2) × s × l Area of one triangular face = (1)/(2) × 6 × sqrt(73) cm^2 Area of one triangular face = 3sqrt(73) cm^2 Step 5: Calculate the total area of the four triangular faces. Since the base is square, there are four identical triangular faces. Total area of triangular faces = 4 × (Area of one triangular face) Total area of triangular faces = 4 × 3sqrt(73) cm^2 Total area of triangular faces = 12sqrt(73) cm^2 Step 6: Calculate the total surface area of the pyramid. Total surface area = Area of base + Total area of triangular faces Total surface area = 36 + 12sqrt(73) cm^2 Step 7: Approximate the value and provide the final answer. sqrt(73) ≈ 8.544 Total surface area ≈ 36 + 12 × 8.544 Total surface area ≈ 36 + 102.528 Total surface area ≈ 138.528 cm^2 The total surface area of the pyramid is 36 + 12sqrt(73) cm^2. 36 + 12sqrt(73) cm^2 Got more? Send 'em 📸