Collection of geometry problems asking students to calculate the volume for nine different prisms, ranging from simple cuboids to triangular and parallelogram shapes.

Let’s solve each prism volume step by step.

Remember:
Volume of a prism = Area of the base × height (or length) of the prism

We’ll go one by one.

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(a) Rectangular prism
Base is rectangle: 4cm × 3cm → area = 12 cm²
Length (height of prism) = 6cm
Volume = 12 × 6 = 72 cm³

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(b) Triangular prism
Base is right triangle: base=6cm, height=5cm → area = (6×5)/2 = 15 cm²
Length of prism = 20cm
Volume = 15 × 20 = 300 cm³

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(c) Triangular prism
Base triangle: base=7m, height=5m → area = (7×5)/2 = 17.5 m²
Length = 4m
Volume = 17.5 × 4 = 70 m³

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(d) Rectangular prism — but units are mixed!
Width = 1.1m, Depth = 40cm = 0.4m, Height = 2m
Better to convert all to meters:
Area of base = 1.1 × 0.4 = 0.44 m²
Height = 2m
Volume = 0.44 × 2 = 0.88 m³

*(Alternatively, convert everything to cm: 1.1m=110cm, 2m=200cm → 110×40×200 = 880,000 cm³ = 0.88 m³ — same answer)*

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(e) Triangular prism
Base triangle: base=7cm, height=8cm → area = (7×8)/2 = 28 cm²
Length = 5.5cm
Volume = 28 × 5.5 = let’s calculate:
28 × 5 = 140, 28 × 0.5 = 14 → total = 154 cm³

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(f) Parallelogram-based prism
Base is parallelogram: base=9cm, height=6cm → area = 9×6 = 54 cm²
Length = 12cm
Volume = 54 × 12 =
54×10=540, 54×2=108 → 540+108 = 648 cm³

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(g) Right triangular prism
Base triangle: legs 5cm and 12cm → area = (5×12)/2 = 30 cm²
Length = 22cm
Volume = 30 × 22 = 660 cm³

*(Note: The 13cm is the hypotenuse — we don’t need it for area since we have perpendicular sides.)*

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(h) Trapezoidal prism? Wait — actually, looking at the diagram:
It shows a trapezoid base? But labels say:
Bottom base = 25cm, top base = ? Not given directly.
Wait — actually, the red dotted line is height=8cm, and there’s a label “10cm” on the side — that might be slant height?
But also, arrows show two parallel sides: bottom 25cm, top... wait, no top labeled.
Actually, re-examining: This looks like a trapezoidal prism, with trapezoid base having:

- Parallel sides: 25cm and ???
Wait — the diagram has “8cm” as height of trapezoid, and “10cm” as the non-parallel side? That doesn’t help unless we know both bases.

Hold on — maybe I misread. Let me look again.

Actually, in many such diagrams, if only one base and height are given for the face, and it's drawn as a rectangle or parallelogram, perhaps it’s intended to be a parallelogram base?

Wait — the figure (h) has:

- A front face that is a parallelogram? With base 25cm, height 8cm (red dotted), and side 10cm (which may be slant).
But for area of parallelogram, we only need base and perpendicular height → so area = 25 × 8 = 200 cm²
Then length of prism = 40cm
Volume = 200 × 40 = 8000 cm³

Yes — even though 10cm is shown, it’s not needed because we’re given the perpendicular height (8cm) for the base area.

So Volume = 25 × 8 × 40 = 8000 cm³

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(i) Triangular prism
Base triangle: base=14cm, height=9cm → area = (14×9)/2 = 63 cm²
Length = 15cm
Volume = 63 × 15 =
60×15=900, 3×15=45 → 900+45 = 945 cm³

*(The 11cm is probably a side of the triangle — not needed since we have base and height.)*

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Now let’s list all answers clearly:

(a) 72 cm³
(b) 300 cm³
(c) 70 m³
(d) 0.88 m³
(e) 154 cm³
(f) 648 cm³
(g) 660 cm³
(h) 8000 cm³
(i) 945 cm³

Double-checking calculations:

- (a) 4×3×6 = 72 ✔️
- (b) (6×5/2)×20 = 15×20=300 ✔️
- (c) (7×5/2)×4 = 17.5×4=70 ✔️
- (d) 1.1×0.4×2 = 0.88 ✔️
- (e) (7×8/2)×5.5 = 28×5.5=154 ✔️
- (f) 9×6×12 = 54×12=648 ✔️
- (g) (5×12/2)×22 = 30×22=660 ✔️
- (h) 25×8×40 = 200×40=8000 ✔️
- (i) (14×9/2)×15 = 63×15=945 ✔️

All correct.

Final Answer:
(a) 72 cm³
(b) 300 cm³
(c) 70 m³
(d) 0.88 m³
(e) 154 cm³
(f) 648 cm³
(g) 660 cm³
(h) 8000 cm³
(i) 945 cm³