A science class builds a triangular prism model. The triangular base has base and height . The prism length is . What is the volume of the triangular prism?
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Explanation: Tests solving area, volume, and surface area problems for composite figures by decomposing into simpler shapes (rectangles, triangles, prisms, pyramids), applying formulas, and combining results. Composite figures: decompose into standard shapes (L-shape as two rectangles: 10×5=50 and 6×3=18, sum: 68; or as large minus cutout: 10×8=80 minus 4×3=12, difference: 68, equivalent). Formulas: triangle A=(1/2)bh, rectangle A=lw, rectangular prism V=lwh, pyramid V=(1/3)Bh (B=base area), triangular prism V=((1/2)bh)×length (triangle base area times prism length). For this triangular prism, first find the triangular base area: A=(1/2)×6×4=12 cm², then multiply by prism length: V=12×10=120 cm³. Common error would be forgetting the (1/2) in the triangle area formula, using 6×4=24 instead of 12, giving volume 240 cm³. Steps: (1) identify shape (triangular prism), (2) calculate triangular base area using A=(1/2)bh=(1/2)×6×4=12 cm², (3) multiply by prism length for volume V=12×10=120 cm³, (4) verify units (volume in cm³). The key is remembering that triangular prism volume equals (triangular base area)×(prism length), and the triangular area requires the factor (1/2).