Question

a solid oblique pyramid has a square base with an edge length of 2 cm. angle bac measures 45° and ac measures 3.6 cm. what is the volume of the pyramid? 2.4 cm³ 3.6 cm³ 4.8 cm³ 7.2 cm³

Explanation:

Step1: Find the area of the base

The base is a square with edge - length $a = 2$ cm. The area of a square $A_{base}=a^{2}$. So, $A_{base}=2^{2}=4$ $cm^{2}$.

Step2: Determine the height of the pyramid

In right - triangle $BAC$, $\angle BAC = 45^{\circ}$ and $AC = 3.6$ cm. Since $\tan\angle BAC=\frac{BC}{AC}$ and $\angle BAC = 45^{\circ}$ (and $\tan45^{\circ}=1$), the height $h$ of the pyramid (equal to $BC$) is $h = 3.6$ cm.

Step3: Calculate the volume of the pyramid

The volume formula of a pyramid is $V=\frac{1}{3}A_{base}h$. Substitute $A_{base}=4$ $cm^{2}$ and $h = 3.6$ cm into the formula. So, $V=\frac{1}{3}\times4\times3.6 = 4.8$ $cm^{3}$.

Answer:

$4.8$ $cm^{3}$