Calculating Surface Area of a Rectangular Pyramid | Geometry

Understanding Surface Area

• 🎯 Lateral surface area refers to the area of the sides of a 3D figure, excluding the base.
• 💡 Total surface area is the lateral surface area plus the area of the base.
• 📐 For a right rectangular pyramid, the peak is directly above the center of the base, meaning opposite triangular faces have equal areas.

Calculating Lateral Surface Area

• ⚡ To find the area of each triangular face, we need its base and height (slant height).
• 🧠 The height of the pyramid is given as 11 m.
• ⚠️ For the faces with a base of 10 m, the distance from the center to the edge is 3 m (half of 6 m). Using the Pythagorean theorem (11² + 3²), the slant height (h) is the square root of 130 m.
• 📐 The area of one of these triangles is 1/2 * 10 * sqrt(130) = 5 * sqrt(130) m².
• ⚠️ For the faces with a base of 6 m, the distance from the center to the edge is 5 m (half of 10 m). Using the Pythagorean theorem (11² + 5²), the slant height (x) is the square root of 146 m.
• 📐 The area of one of these triangles is 1/2 * 6 * sqrt(146) = 3 * sqrt(146) m².
• ➕ The total lateral surface area is the sum of the areas of all four triangular faces: 2 * (5 * sqrt(130)) + 2 * (3 * sqrt(146)) = 10 * sqrt(130) + 6 * sqrt(146) m².

Calculating Total Surface Area

• ➕ To find the total surface area, add the lateral surface area to the area of the rectangular base.
• 📏 The base area is calculated by multiplying its dimensions: 10 m * 6 m = 60 m².
• ➡️ Total Surface Area = (10 * sqrt(130) + 6 * sqrt(146)) + 60 m².