In a regular triangular prism, the side of the base is 5cm, height is 3cm. find: volume and area.

Since the prism is regular, its bases are equilateral triangles with an edge of 5 cm.

Determine the area of the base of the prism.

Sbn = AB ^ 2 * √3 / 4 = 25 * √3 / 4 cm2.

Then the volume of the prism is: V = Sax * AA1 = 3 * 25 * √3 / 4 = 75 * √3 / 4 cm3.

Let’s calculate the area of the lateral surface of the prism.

Sside = Rosn * AA1 = 15 * 3 = 45 cm2.

Then Sпов = 2 * Sсн + S side = 2 * (25 * √3 / 4) + 45 = 45 + 25 * √3 / 2 = 5 * (9 + 5 * √3 / 2) cm2.

Answer: The volume of the prism is 75 * √3 / 4 cm3., The area is (9 + 5 * √3 / 2) cm2.