To find the surface area of a right triangular prism, we need to find the areas of all the faces and sum them up.
The base of the prism is a right-angled triangle. Let's find its area first.
The formula for the area of a right-angled triangle is (1/2) * base * height. In this case, the base is one of the edges, which measures 15.10 cm, and the height can be found using the Pythagorean theorem. The Pythagorean theorem states that for a right-angled triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. In this case, the two legs are both edges of length 15.10 cm, so we can solve for the height (h) using the equation: h^2 = 15.10^2 + 15.10^2.
h^2 = 228.01 + 228.01
h^2 = 456.02
h = √456.02
h ≈ 21.36 cm (rounded to two decimal places)
The area of the base is (1/2) * 15.10 * 21.36 ≈ 160.92 cm^2.
Now, let's find the areas of the two triangular faces. Each triangle has a base of 15.10 cm and a height of 21.36 cm. The area of each triangle is (1/2) * 15.10 * 21.36 = 161.07 cm^2.
Finally, the areas of the three rectangular faces can be found by multiplying the length of one edge by the height of each face. Each face has a height of 21.36 cm, so the areas of the three rectangular faces are 15.10 * 21.36 = 322.62 cm^2, 15.10 * 21.36 = 322.62 cm^2, and 15.10 * 15.10 = 227.01 cm^2.
Summing up the areas of all the faces, we get: 160.92 + 161.07 + 161.07 + 322.62 + 322.62 + 227.01 = 1,355.31 cm^2.
Therefore, the correct option is B. 1,350 cm^2.
What is the surface area of a right triangular prism where each edge length measures 15.10 cm?
A. 1,368.06^2
B. 1,350 cm^2
C. 900 cm^2
D. 8,208.36 cm^2
1 answer