Colton has a stone paperweight composed of a triangular pyramid on top of a triangular prism with the dimensions shown below. Use the drop-down menus to explain how to determine the volume of the paperweight. Needdddd major hellllpppp pleaseeee!!!!! 40 points!!!

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musiclover10045 musiclover10045 · Answer 1 · 2020-08-22T02:45:24+02:00

The area of the base would be found using the area of a triangle formula which is 1/2 x base x height.

The base and height are the two sides perpendicular to each other, which are both 5 inches.

The area of the base = 1/2 x 5 x 5 = 12.5 square inches.

The volume of the triangular prism is the area of the base times the height, which is 4 inches.

Volume of the triangular prism is 12.5 x 4 = 50 cubic inches.

Volume of the triangular prism is 1/3 x area of base x height, which is 7:

Volume of the triangular prism = 1/3 x 12.5 x 7 = 29.17 cubic inches.

Total volume = 29.17 + 50 = 79.17 cubic inches.

MrRoyal MrRoyal · Answer 2 · 2022-01-12T03:40:53+01:00

The complete statements are:

The area of the base of the prism is equal to the area of the base of the pyramid which can be determined by multiplying half the base and the height
To find the volume of the triangular prism, multiply the area of the base by 4
To find the volume of the triangular pyramid, multiply the area of the base by 1/3 of 7
The volume of the paperweight is approximately 79.17 cubic inches

Start by calculating the area of the base of the pyramid using:

[tex]A_1 = \frac 12 \times base \times height[/tex]

So, we have:

[tex]A_1 = \frac 12 \times 5 \times 5[/tex]

[tex]A_1 = 12.5[/tex]

The volume of the triangular prism is then calculated using:

[tex]V_1 = A_1 \times h[/tex] --- i.e. the product of area and height (4)

So, we have:

[tex]V_1 = 12.5 \times 4[/tex]

[tex]V_1 = 50[/tex]

The volume of the triangular pyramid is then calculated using:

[tex]V_2 = \frac 13 \times A_1 \times h_2[/tex] --- i.e. the product of 1/3 of the area and height (7)

So, we have:

[tex]V_2 = \frac 13 \times 12.5 \times 7[/tex]

[tex]V_2 = 29.17[/tex]

The total volume of the shape is then as:

[tex]V = V_1 + V_2[/tex]

[tex]V = 50 + 29.17[/tex]

[tex]V = 79.17[/tex]

Hence, the volume of the paperweight is approximately 79.17 cubic inches