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Sagot :
Answer:
1.28 cubic meters
Step-by-step explanation:
You want the volume of the pentagonal prism shown.
End area
The area of a pentagonal face of the doghouse is that of a triangle together with a rectangle. It will be the same as that of a trapezoid of the same width with one base equal to the full height, and the other base equal to the rectangle height.
A = triangle + rectangle
A = (1/2)(1.2 -0.7)(0.9) +(0.7)(0.9)
A = (1/2)(1.2 +0.7)(0.9)
Volume
The volume is the product of the end area and the length of the doghouse.
V = Bh . . . . . . where B is the area of the base, and h is the "height" (length) of the prism
V = (1/2)(1.2 +0.7)(0.9)(1.5) = 1.2825 . . . . cubic meters
The volume of the doghouse is about 1.28 cubic meters.
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Additional comment
As you know from the formula for the area of a triangle, its area is equivalent to that of a rectangle with the same base and half the height. That makes it convenient to redraw the figure as being a cuboid with height equal to the average of the 70 cm dimension and the 1.2 m dimension.
Answer:
1.28m³
Step-by-step explanation:
Sirius' doghouse structure into two parts:
Upper structure and the base structure.
Volume of the upper structure = volume of a prism with isosceles base triangle.
Volume of the upper structure = base area × height of the prism
= 2 × 1/2bh × height of the prism
= bh × height of the prism
= 0.45m × 0.5m × 1.5m
= 0.3375m³
Volume of the base structure =
volume of a rectangular prism
= length × width × height
= 1.5 × 0.9 × 0.7
= 0.945m³
Therefore, the volume of Sirius' doghouse
= Volume of the upper structure + Volume of the base structure
= 0.3375m³ + 0.945m³
= 1.2825 m³
= 1.28m³ to the nearest hundredth.
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