Find the requested measurements for the shape below (3 points)
A triangular prism as a height of 10 cm a triangle length od 10 cm and a rectangle length of 25cm
Lateral Surface area = Response area Total Surface Area = Response area Volume = Response area
Answer Choises:
852.5
688.1
952.5
1250
1014.7
734.8
Given measurements:
Height (h) = 10 cm
Triangle length (l) = 10 cm
Rectangle length (L) = 25 cm
To find the lateral surface area of a triangular prism, we need to calculate the area of the two triangles and the rectangle.
Area of a triangle = (1/2) x base x height
Area of first triangle = (1/2) x 10 cm x 10 cm = 50 cm^2
Area of second triangle = (1/2) x 10 cm x 10 cm = 50 cm^2
Area of rectangle = length x width = 25 cm x 10 cm = 250 cm^2
Lateral surface area = 2 x area of triangle + area of rectangle
Lateral surface area = 2(50 cm^2) + 250 cm^2
Lateral surface area = 100 cm^2 + 250 cm^2
Lateral surface area = 350 cm^2
Next, to find the total surface area of the triangular prism, we need to add the two triangular bases as well.
Total surface area = Lateral surface area + 2 x area of triangle
Total surface area = 350 cm^2 + 2(50 cm^2)
Total surface area = 350 cm^2 + 100 cm^2
Total surface area = 450 cm^2
Finally, to find the volume of the triangular prism, we calculate the area of the base triangle and multiply it by the height.
Area of base triangle = (1/2) x base x height = (1/2) x 10 cm x 10 cm = 50 cm^2
Volume = area of base triangle x height
Volume = 50 cm^2 x 10 cm
Volume = 500 cm^3
Therefore, the measurements for the given triangular prism are:
Lateral Surface Area = 350 cm^2
Total Surface Area = 450 cm^2
Volume = 500 cm^3
None of the provided answer choices match the calculated measurements.