To find the surface area of a rectangular pyramid, we need to calculate the areas of its five faces: the base and the four triangular faces.
First, let's calculate the area of the base. Since it is a rectangle, we can use the formula: Area = length × width.
Area of the base = 13 × 11 = 143.
Next, let's calculate the area of the four triangular faces. Each triangular face can be thought of as a right triangle, with one leg being the slant height and the other leg being half the length or width of the base.
To find the slant height, we can use the Pythagorean theorem. In a right triangle formed by the slant height, the height, and the half the length of the base, the slant height is the hypotenuse.
Using the height (8), half the length of the base (13/2 = 6.5), and the Pythagorean theorem:
slant height^2 = height^2 + (base/2)^2
slant height^2 = 8^2 + 6.5^2
slant height^2 = 64 + 42.25
slant height^2 = 106.25
slant height ≈ √106.25
slant height ≈ 10.31
Now, we can calculate the area of each triangular face using the formula: Area = 0.5 × base × height.
Area of each triangular face = 0.5 × 11 × 10.31 ≈ 56.71 (rounded to two decimal places since we will round the final answer to the nearest hundred).
Finally, let's calculate the surface area by adding up the area of the base and the four triangular faces:
Surface area = Area of the base + 4 × Area of each triangular face
Surface area = 143 + 4 × 56.71
Surface area = 143 + 226.84
Surface area ≈ 369.84
Therefore, the surface area of the rectangular pyramid is approximately 369.84, rounded to the nearest hundred.
Find the surface area of a rectangular pyramid with the measurements length 13 width 11 height eight express your answer is a decimal rounded the nearest hundred
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