Find the requested measurements for the shape below (3 points)

Question

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: (USE THEZSE)
852.5
688.1
952.5
1250
1014.7
734.8

Answer 1

To calculate the lateral surface area, total surface area, and volume of the triangular prism, we will first break down the shape into its individual parts.

The triangular prism consists of two triangular bases and three rectangular sides.

1. Lateral Surface Area:
The lateral surface area of a prism can be calculated by finding the perimeter of the base and multiplying it by the height of the prism. In this case, the base of the prism is a triangle with sides of 10 cm, 10 cm, and 25 cm. The perimeter of the base triangle = 10 + 10 + 25 = 45 cm.

Lateral Surface Area = Perimeter of base * Height
Lateral Surface Area = 45 cm * 10 cm
Lateral Surface Area = 450 cm^2

2. Total Surface Area:
The total surface area of a prism is the sum of the lateral surface area and the areas of the two bases. Since the base of the prism is a triangle, we need to calculate the area of the triangle.

The area of a triangle can be calculated using Heron's formula:
Area = √(s * (s - a) * (s - b) * (s - c))
where s = (a + b + c) / 2

In this case, a = 10 cm, b = 10 cm, and c = 25 cm.
s = (10 + 10 + 25) / 2 = 45 / 2 = 22.5

Area of the base triangle = √(22.5 * (22.5 - 10) * (22.5 - 10) * (22.5 - 25))
Area of the base triangle = √(22.5 * 12.5 * 12.5 * -2.5)
Area of the base triangle = √(22.5 * 3125)
Area of the base triangle = √70312.5
Area of the base triangle ≈ 265.2 cm^2

Total Surface Area = Lateral Surface Area + 2 * Area of base
Total Surface Area = 450 cm^2 + 2 * 265.2 cm^2
Total Surface Area = 450 cm^2 + 530.4 cm^2
Total Surface Area = 980.4 cm^2

3. Volume:
The volume of a prism can be calculated by multiplying the area of the base by the height of the prism.

Volume = Area of base * Height
Volume = 265.2 cm^2 * 10 cm
Volume = 2652 cm^3

Therefore, the measurements for the given triangular prism are:
Lateral Surface Area = 450 cm^2
Total Surface Area = 980.4 cm^2
Volume = 2652 cm^3

Therefore, the answer choice closest to these values is 952.5, but the exact calculations do not match any of the given answer choices.