1) Determine the volume of a triangular prism not right in which the base has sides of $26 cm$, $28cm$ and $30cm$. One lateral edge is $52 cm$ and it's projection on the plane of the base is 20 cm.
2)The base of a parallelepiped is a rectangle $ABCD$ in which $AB:BC=5:2$ and $AC=6\sqrt{29}$ cm. The height of the parallelepiped is $8cm$ and the projection of the summit $A'$ of the upper base, on the lower base, conincide with the meeting point $O$ of the diagonals. Determine the lateral area and volume.
In the first problem I have determined the area of the triangle with the formula of Erone, and it is 336 $cm^2$. So to determine the volume I did $V=A_{b}\cdot h=336cm^2\cdot 20cm=6720 cm^3$ but the result is 16128$cm^3$. Where is the mistake?
In the second problem I have determined the sides of the base, $AB=30 cm$ and $BC=12 cm$, so the perimeter of the rectangle is 84cm. Since half of a diagonal of the rectangle is $A0=3\sqrt{29}cm$ and $A'O=8cm$, I have determined $AA'=5\sqrt{13}cm$, but how can I find the lateral area?
The altitude of our prism is $$\sqrt{52^2-20^2}=4\sqrt{13^2-5^2}=4\cdot12=48$$ and the area of the base it's indeed,$336.$
Thus, $V=336\cdot48=16128.$
The hint for the second problem.
Let $K$ and $M$ be midpoints of $AD$ and $AB$ respectively.
Thus, $A'M$ and $A'K$ are altitudes of parallelograms $ABB'A'$ and $ADD'A'$.
I am sure that you'll end the solution by yourself.