Answer: 475 cm^2.
Step-by-step explanation:
Surface Area = base area + (1/2 x perimeter x slant height)
First, let's find the base area of the pyramid:
Base area = length x width
Base area = 10 cm x 15 cm
Base area = 150 cm^2
Next, let's find the slant height of the pyramid using the Pythagorean theorem:
a^2 + b^2 = c^2
(1/2 x 10 cm)^2 + 12 cm^2 = h^2
25 cm^2 + 144 cm^2 = h^2
169 cm^2 = h^2
h = √169 cm
h = 13 cm
Now, let's find the perimeter of the base:
Perimeter = 2(length + width)
Perimeter = 2(10 cm + 15 cm)
Perimeter = 50 cm
Finally, let's plug in the values we found into the formula for surface area:
Surface Area = 150 cm^2 + (1/2 x 50 cm x 13 cm)
Surface Area = 150 cm^2 + 325 cm^2
Surface Area = 475 cm^2
Therefore, the surface area of the pyramid is 475 cm^2.
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Answers & Comments
Answer: 475 cm^2.
Step-by-step explanation:
Surface Area = base area + (1/2 x perimeter x slant height)
First, let's find the base area of the pyramid:
Base area = length x width
Base area = 10 cm x 15 cm
Base area = 150 cm^2
Next, let's find the slant height of the pyramid using the Pythagorean theorem:
a^2 + b^2 = c^2
(1/2 x 10 cm)^2 + 12 cm^2 = h^2
25 cm^2 + 144 cm^2 = h^2
169 cm^2 = h^2
h = √169 cm
h = 13 cm
Now, let's find the perimeter of the base:
Perimeter = 2(length + width)
Perimeter = 2(10 cm + 15 cm)
Perimeter = 50 cm
Finally, let's plug in the values we found into the formula for surface area:
Surface Area = base area + (1/2 x perimeter x slant height)
Surface Area = 150 cm^2 + (1/2 x 50 cm x 13 cm)
Surface Area = 150 cm^2 + 325 cm^2
Surface Area = 475 cm^2
Therefore, the surface area of the pyramid is 475 cm^2.