6. ABCD is a quadrilateral, and AC and BD are its diagonals. Is \( \mathrm{AB}+\mathrm{BC}+\mathrm{CD}+\mathrm{DA}>\mathrm{AC}+\mathrm{BD} \) ? 7. ABCD is a quadrilateral and \( O \) is any point in its interior in the given figure Show that \( A B+B C+C D+D A<2(O A+O B+O C+O D) \).

A triangular prism has a base area of 30 square centimeters and a height of 10 centimeters. Calculate the volume of this triangular prism and then compare it to the volume of a triangular pyramid with the same base area and height.

Dado un cilindro con un radio de 4 cm, ¿cuál debe ser la altura para que el volumen sea \( 64\pi \) cm³?

the area of \( \triangle A B C=12 \mathrm{~cm}^{2} \), then \( \left(b^{2}+c^{2}-a^{2}\right) \tan A=\cdots \) 12 (b) 24

A square prism measuring 2 m by 2 m in base length and 5 m in height has a half-sphere attached to the top. What is the total surface area of this composite solid?

3) The exterior bisector of the vertex angle of an isosceles triangle \( \cdots \cdots . . . \). the base. \( \begin{array}{ll}\text { (a) bisects } & \text { (b) perpendicular to } \\ \text { (c) intersect } & \text { (d) parallel }\end{array} \)