1 La base di un triangolo misura 14.7 cm , la sua altezza misura 14.4 cm e gli altri due lati misurano 15 cm e 18 cm . Calcola: (a) I'area del triangolo. (b) il perimetro del triangolo.

Calculate the combined volume of a cone with a base radius of 4 cm and height of 9 cm, and a cube with side length of 6 cm.

24) ABC is a triangle in which \( \mathrm{m}(\angle \mathrm{A})=60^{\circ}, \mathrm{b}: \mathrm{c}=5: 8 \) and the area of the circumcircle of the triangle ABC is \( 147 \pi \mathrm{~cm}^{2} \), then the perimeter of \( \triangle \mathrm{ABC}=\ldots \ldots \ldots \cdots \cdot \mathrm{cm} \). \( \begin{array}{llll}\text { (a) } 21 & \text { (b) } 34 & \text { (c) } 54 & \text { (d) } 60\end{array} \)

4a If \( (0,1),(a, 3),(2,5) \) are collinear, find the value of a

Denise is constructing a square in which two of its vertices are points \( M \) and \( N \). She has already used her straightedge and compass to construct the lines and arcs shown. What should Denise do for her next step? Place the point of the compass on point \( M \) and draw any arc above it. Use a straightedge to draw Place the point of the compass on point \( N \) and draw an arc that intersects width for the opening of the compass. Use a straightedge to draw a horizontal line that contains point \( O \).

b) Prove the following by vector method. Measure of the angle between two diagonals of a cube is \( \cos ^{-1} \frac{1}{3} \)