The legs of a right triangular prism measure 9 inches and 12 inches. The prism has a height of 5 inches. What is the surface area of the prism?
the two bases have area 9*12/2 = 54
the three lateral faces are rectangles, with height 5, and width equal to the sides of the right triangle.
So now you just have to determine the hypotenuse of a scaled-up 3-4-5 right triangle (or use the Pythagorean Theorem, if you must).
thank you so much oobleck for your help!
To find the surface area of a right triangular prism, we need to calculate the area of each face and add them together.
First, let's find the area of the triangular base of the prism. We can use the formula for the area of a triangle: A = 1/2 * base * height.
The base of the triangle is one of the legs of the prism, which measures 9 inches, and the height is the other leg, which measures 12 inches.
A = 1/2 * 9 inches * 12 inches = 54 square inches.
Since the prism has two triangular bases, the total area of the triangular bases is 2 * 54 square inches = 108 square inches.
Next, let's find the area of the three rectangular faces of the prism. The formula for finding the area of a rectangle is A = length * width.
The length of the rectangular faces is equal to the height of the prism, which is 5 inches. The width can be found from the other two legs of the prism.
The width of the rectangular face can be found by using the Pythagorean theorem (a^2 + b^2 = c^2) with the legs of the prism. Here, the legs are 9 inches and 12 inches.
c^2 = 9^2 + 12^2 = 81 + 144 = 225. Therefore, c = √225 = 15 inches.
Since the prism has three rectangular faces, the total area of the rectangular faces is 3 * (5 inches * 15 inches) = 225 square inches.
Finally, to find the surface area of the prism, we add the areas of the triangular bases and the rectangular faces together: 108 square inches + 225 square inches = 333 square inches.
Therefore, the surface area of the right triangular prism is 333 square inches.