Calculate 23411

The prism with a diamond base has one base diagonal of 20 cm and a base edge of 26 cm. The edge of the base is 2:3 to the height of the prism. Calculate the volume of the prism.

Correct answer:

V =  18720 cm³

Step-by-step explanation:

$$\begin{gathered} u=20\text{cm} \\ a=26\text{cm} \\ s=\frac{a+a+u}{2}=\frac{26+26+20}{2}=36\text{cm} \\ {S}_1=\sqrt{s\cdot (s-a)\cdot (s-a)\cdot (s-u)}=\sqrt{36\cdot (36-26)\cdot (36-26)\cdot (36-20)}=240{\text{cm}}^2 \\ S=2\cdot S_1=2\cdot 240=480{\text{cm}}^2 \\ a:v=2:3 \\ v=\frac{3}{2}\cdot a=\frac{3}{2}\cdot 26=\frac{3\cdot 26}{2}=\frac{78}{2}=39\text{cm} \\ V=S\cdot v=480\cdot 39=18720{\text{cm}}^3 \end{gathered}$$

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