What is the area of the slanted rectangle face of this triangular prism?
5cm 5cm 3cm 4cm
We need to find the area of the rectangle, which is one of the two faces that are parallel to each other. To do this, we need to find the length and width of the rectangle.
The length of the rectangle is the same as the length of the triangle's base, which is 5cm.
To find the width of the rectangle, we need to look at one of the triangle's perpendicular sides. The width of the rectangle is the same as the height of the triangle, which is 4cm.
Therefore, the area of the slanted rectangle face is:
Area = length x width
Area = 5cm x 4cm
Area = 20cm²
So the area of the slanted rectangle face is 20cm².
To find the area of the slanted rectangle face of this triangular prism, we need to calculate the area of the base triangle first.
Using the given measurements, the base triangle of the prism has sides of length 5 cm, 5 cm, and 4 cm. To find the area of this triangle, we can use Heron's formula.
Heron's formula states that the area (A) of a triangle with sides of length a, b, and c can be calculated using the semi-perimeter (s):
s = (a + b + c)/2
Then, the area can be calculated as:
A = √(s(s-a)(s-b)(s-c))
In this case, a = 5 cm, b = 5 cm, and c = 4 cm. Let's calculate the area:
s = (5 + 5 + 4)/2 = 14/2 = 7
A = √(7(7-5)(7-5)(7-4))
= √(7(2)(2)(3))
= √(84)
≈ 9.17 cm^2
Now that we have the area of the base triangle, let's calculate the area of the slanted rectangle face. The slanted rectangle connects two vertices of the base triangle and is perpendicular to the height of the prism.
Since the height of the prism is given as 3 cm, the length of the slanted rectangle face is equal to the height. Thus, the area of the slanted rectangle face is:
Area = Base × Height
= 9.17 cm^2 × 3 cm
≈ 27.51 cm^2
Therefore, the area of the slanted rectangle face of this triangular prism is approximately 27.51 cm^2.