Step-by-step explanation:
2 basic objects are combined to this figure.
a prism or box of 20×8×18
a diagonally cut box (so, triangle shaped) of 8×18 base area and 10 being the triangle Hypotenuse.
the volume of the box is easy :
20×8×18 = 2,880
for the triangle-shaped half-box we need to get the height (the third leg of the side triangle).
we get this by Pythagoras
Hypotenuse² = leg1² + leg2²
10² = 8² + height²
100 = 64 = height²
36 = height²
height = 6
so, the area of a side triangle is
8×6/2 = 8×3 = 24
and the volume of the half-box is
24 × 18 = 432
so, the total volume of the figure is
2,880 + 432 = 3,312
