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Hey there! Ready to explore 3D shapes? Today we will learn how to find the total surface area of prisms and pyramids by unfolding them!
Think of surface area as the amount of wrapping paper you need to cover a solid 3D shape. To find it, we calculate the area of every single flat face and add them all together.
Imagine unfolding a cardboard box. This flat, 2D layout of a 3D shape is called a 'net'. A rectangular prism unfolds into six flat rectangles.
A pyramid has a flat base and triangular sides that meet at a top point. When we unfold a square pyramid, we get one square base in the middle and four identical triangles pointing outward.
Find the total surface area of a square pyramid. The square base has side lengths of 6 cm. Each of the four triangular faces has a height (slant height) of 8 cm.
- Step 1: Identify the shapes in the net. We have 1 square base and 4 identical triangles.
- Step 2: Find the area of the square base. Area = side times side, so 6 cm x 6 cm = 36 square cm.
- Step 3: Find the area of one triangular face. Area = (base x height) / 2, so (6 cm x 8 cm) / 2 = 24 square cm.
- Step 4: Multiply the triangle's area by 4, since there are four identical triangular faces: 24 square cm x 4 = 96 square cm.
- Step 5: Add the base area and the total triangular area together: 36 + 96 = 132 square cm. The total surface area is 132 square cm!
