Answer :

sqdancefan

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.

__

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.

View image sqdancefan
olumideolawoyin

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.

View image olumideolawoyin