a solid oblique pyramid has a square base with an edge length of 2 cm. angle bac measures 45° and ac…

Explanation:

Step1: Find the base - area of the pyramid

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

Step2: Find the height of the pyramid

In right - triangle (ABC), (\angle BAC = 45^{\circ}) and (AC = 3.6\mathrm{cm}). Since (\tan\angle BAC=\frac{BC}{AC}) and (\angle BAC = 45^{\circ}), (\tan45^{\circ}=1=\frac{BC}{AC}), so the height (h = BC=3.6\mathrm{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\mathrm{cm}^{2}) and (h = 3.6\mathrm{cm}) into the formula: (V=\frac{1}{3}\times4\times3.6 = 4.8\mathrm{cm}^{3}).

Answer:

(4.8\mathrm{cm}^{3})