Answer:
- volume: 240 cm³
- area: 252 cm²
Step-by-step explanation:
You have a prism with a height of 8 cm and a cross section in the shape of a trapezium with bases 9 cm and 6 cm, and height 4 cm, and you want to know its volume and area.
Figure
We interpret the figure as having an error in the placement of the "6 cm" dimension. We imagine it belongs next to the upper-right segment indicating the top edge is 3 cm shorter than the 9 cm bottom edge. Our understanding of the net for the figure is attached.
Volume
The area of each trapezium base is ...
A = 1/2(b1 +b2)h
A = 1/2(9 cm +6 cm)(4 cm) = 30 cm²
The distance between the bases is 8 cm, so the volume is ...
V = Bh = (30 cm²)(8 cm) = 240 cm³ . . . . prism volume
Area
The attached net shows the lateral area to be that of a rectangle 8 cm wide and 4+9+5+6 = 24 cm long.
lateral area = (8 cm)(24 cm) = 192 cm²
The area of one base was found above, so the area of both bases is ...
total base area = 2 × 30 cm² = 60 cm²
Then the total surface area of the figure is ...
TSA = LA +BA
TSA = 192 cm² +60 cm² = 252 cm² . . . . total surface area
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Additional comment
The 6 cm top edge makes the slant length of 5 cm be the hypotenuse of a 3-4-5 right triangle. This supports our suspicion that the figure is mislabeled.
