Answer:
[tex]42[/tex]
Step-by-step explanation:
The area of a triangle with base [tex]b[/tex] and height [tex]h[/tex] is given by [tex]A=\frac{1}{2}bh[/tex]. In the trapezoid, the two triangles share a height of 6, however one has a base of 6 and the other has a base of 8.
Area of smaller triangle (triangle on the left): [tex]\frac{1}{2}\cdot 6 \cdot 6=18\:\mathrm{cm^2}[/tex]
Area of larger triangle (triangle on the right): [tex]\frac{1}{2}\cdot 8 \cdot 6=24\:\mathrm{cm^2}[/tex]
Therefore, the sum of their areas are [tex]18+24=\boxed{42\:\mathrm{cm^2}}[/tex]
