To find the lateral area of a triangular prism, you can use the formula: lateral area = perimeter of base x height of prism.
First, calculate the perimeter of the base triangle:
perimeter = 2m + 5m + 5.39m = 12.39m
Next, plug in the values into the formula:
lateral area = 12.39m x 26m = 322.14m²
Rounded to the nearest whole number, the lateral area is 322 m².
To find the surface area of the triangular prism, you can use the formula: surface area = lateral area + 2(base area).
The base area of a triangle is calculated using Heron's formula:
s = (2m + 5m + 5.39m) / 2 = 6.695m
base area = √(6.695m * (6.695m - 2m) * (6.695m - 5m) * (6.695m - 5.39m)) ≈ 5.249m²
Now, plug in the values into the surface area formula:
surface area = 322.14m² + 2(5.249m²) = 322.14m² + 10.498m² = 332.638m²
Rounded to the nearest whole number, the surface area is 333 m².
Therefore, the answers are:
322 m²; 333 m².
Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
A right triangular prism is shown. The legs of the right triangle base measure 2 meters and 5 meters. The hypotenuse measures 5.39 meters. The height of the prism is 26 meters.
(1 point)
Responses
322 m2; 327 m2
322 m 2 ; 327 m 2
296 m2; 342 m2
296 m 2 ; 342 m 2
296 m2; 332 m2
296 m 2 ; 332 m 2
322 m2; 332 m2
1 answer
1 answer