To find the surface area of a square pyramid, we need to add the area of the base to the area of the four triangular faces.
The surface area of the base can be found by squaring the length of one side of the square. In this case, the length of one side of the square base is 0.5 cm. So, the area of the base is 0.5 cm * 0.5 cm = 0.25 square cm.
The surface area of each triangular face can be found using the formula (1/2) * base * height, where the base is the length of one side of the square and the height is the slant height of the pyramid.
The slant height can be found using the Pythagorean theorem, where the hypotenuse is the slant height and the legs are the height of the triangle (l) and half the length of one side of the square (0.5/2 = 0.25 cm).
Using the Pythagorean theorem:
slant height^2 = height^2 + (0.25 cm)^2
slant height^2 = 0.8 cm^2 + 0.0625 cm^2
slant height^2 = 0.8625 cm^2
slant height = √0.8625 cm^2 ≈ 0.93 cm (rounded to two decimal places)
Now, we can calculate the surface area of each triangular face:
surface area of each triangular face = (1/2) * base * height
surface area of each triangular face = (1/2) * 0.5 cm * 0.93 cm ≈ 0.23 square cm (rounded to two decimal places)
Since there are four triangular faces, the total surface area of the pyramid is:
total surface area = base area + 4 * triangular face area
total surface area = 0.25 square cm + 4 * 0.23 square cm = 0.25 square cm + 0.92 square cm = 1.17 square cm.
Therefore, the surface area of the square pyramid with a = 0.5 cm and l = 0.8 cm is approximately 1.17 square cm.
UNITS ARE NEEDED FOR FULL CREDIT
Find the surface area of a square pyramid with “a” of .5cm and “l” of .8cm, round to tenth and proper units.
1 answer