Question

the volume of a prism is 300cm^3 and the base area is 50cm^2. whats the height? 4cm 5cm 6cm 8cm what is the area of a triangle with base 12 cm and height 8 cm? 48cm^2 96cm^2 72cm^2 36cm^2

Explanation:

Step1: Recall the volume formula for a prism

The volume formula for a prism is \(V = B\times h\), where \(V\) is the volume, \(B\) is the base area, and \(h\) is the height. Given \(V = 300\mathrm{cm}^3\) and \(B=50\mathrm{cm}^2\), we can solve for \(h\) by rearranging the formula to \(h=\frac{V}{B}\).

Step2: Calculate the height of the prism

Substitute the values into the formula: \(h=\frac{300}{50}=6\mathrm{cm}\).

Step3: Recall the area formula for a triangle

The area formula for a triangle is \(A=\frac{1}{2}\times b\times h\), where \(b\) is the base and \(h\) is the height. Given \(b = 12\mathrm{cm}\) and \(h = 8\mathrm{cm}\).

Step4: Calculate the area of the triangle

Substitute the values into the formula: \(A=\frac{1}{2}\times12\times8 = 6\times8=48\mathrm{cm}^2\).

Answer:

For the prism height: \(6\mathrm{cm}\) (third option).
For the triangle area: \(48\mathrm{cm}^2\) (first option).