To find the surface area of a rectangular pyramid, we calculate the area of the base and the area of each triangular face and then add them together.
The base of the pyramid is a rectangle with a length of 20 cm and a width of 18 cm. The area of the base is 20 cm * 18 cm = 360 cm².
Next, we need to calculate the area of each triangular face. The height of the pyramid (from the apex to the center of the base) is given as 17.2 cm. The slant height of each triangular face can be calculated using the Pythagorean theorem:
Slant height = √( (1/2 base length)² + height² )
Slant height = √( (9)² + (17.2)² )
Slant height ≈ √(81 + 295.84) ≈ √376.84 ≈ 19.4 cm
Now, we can calculate the area of one triangular face:
Area of one triangular face = (1/2 base length) * slant height
Area of one triangular face = (1/2 * 18) * 19.4
Area of one triangular face ≈ 9 * 19.4 ≈ 174.6 cm²
Since there are 4 triangular faces on a rectangular pyramid, the total surface area is:
Total surface area = Base area + 4(Triangular face area)
Total surface area = 360 + 4 * 174.6 ≈ 360 + 698.4 ≈ 1058.4 cm²
Therefore, the surface area of the rectangular pyramid is approximately 1058.4 cm².
What is the surface of the rectangular pyramid? the rectangular pyramid has a length of 20cm and a width of 18cm and a width height of 17.2 cm and a length height of 16.6cm
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