Answer:
2. 18 cubic cm.
3. 27 cubic cm
5. 90 cubic m
Step-by-step explanation:
2. Triangular prism
So, we have a triangular prism with a width of 3 cm, a height of 1.5 cm and a length of 4. We'll take the triangle shape as the base.
Like for any prism, the volume is the base multiplied by the height.
So, the area of the base is found with the regular formula: base x height:
so, 3 x 1.5 = 4.5 sq cm for the base.
Then we multiply the base by the length to get the volume: 4.5 x 4 = 18 cubic cm.
3. Trapezoidal prism
Again, first step is to calculate the area of the trapezoid shape, then multiply by its depth.
The area of a trapezoid is calculated with the formula:
A = h/2 * (a + b) where a and b represent the short and long sides respectively.
So, for our given trapezoid:
A = 1.5/2 * (2+4) = 0.75 * 6 = 4.5 sq cm.
Then we multiply the base area by the height to get the volume:
V = 4.5 * 6 = 27 cubic cm
5. Triangular prism 2
The best way to approach this one is to consider it's a triangle prism with a height of 3 cm, and use the triangle shape (with sides of 13 and 5) as the base.
But to calculate the area of that triangle we need to find out the missing length. Using Pythagore's theorem, we can easily find the length of the other side with the hypotenuse formula:
hypotenuse² = sideA² + sideB²
In our case, we have:
13² = x² + 5²
169 = x² + 25
x² = 144
x = 12
Now we can calculate the area of the triangle easily:
A = (b x h)/2 = (5 x 12)/2 = 30 sq m
Then multiply by the thickness of the prism....
V = 30 x 3 = 90 cubic m
because you multiply fractions straight across.