Question

What is the volume of the figure below if a = 4.2 units, b = 5.3 units, and c = 2 units?

Answer 1

To find the volume of the figure below, we need to first calculate the area of the base, which is a triangle with sides of length a, b, and c.

Using Heron's formula, the area of the triangle can be calculated as:
Area = sqrt[s(s-a)(s-b)(s-c)]
where s is the semi-perimeter of the triangle given by:
s = (a + b + c) / 2

Plugging in the values:
s = (4.2 + 5.3 + 2) / 2 = 5.25
Area = sqrt[5.25(5.25-4.2)(5.25-5.3)(5.25-2)]
Area = sqrt[5.25 * 1.05 * 0.95 * 3.25]
Area = sqrt(18.51)

Next, we need to find the height of the figure. The height can be found using the Pythagorean theorem:
h = sqrt(b^2 - (0.5*c)^2)
h = sqrt(5.3^2 - (0.5*2)^2)
h = sqrt(28.09 - 2.25)
h = sqrt(25.84)

Finally, we can calculate the volume of the figure:
Volume = (Area * height) / 3
Volume = (sqrt(18.51) * sqrt(25.84)) / 3
Volume = (4.301 * 5.08) / 3
Volume = 0.81 units^3

Therefore, the volume of the figure is 0.81 cubic units.