Gabriel makes a model of a pyramid with the dimensions shown. A square pyramid. The square base has side lengths of 12 inches. The triangul

Question

Gabriel makes a model of a pyramid with the dimensions shown. A square pyramid. The square base has side lengths of 12 inches. The triangular sides have a height of 11 inches. Gabriel wants to paint the model. How much paint will he need? The area of the square base is in.2. The area of each triangular face is in.2. Gabriel will need in.2 of paint.

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Sarah 1 week 2021-11-24T00:02:17+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-24T00:03:33+00:00

    Answer:

    The area of the square base is 144 in²

    The area of each triangular face is 66 in²

    Gabriel will need 408 in² of paint.

    Step-by-step explanation:

    The area of the square base is:

    12² = 144 in²

    The area of each triangular face:

    ½(12×11) = 66 in²

    Gabriel will need:

    4(66) + 144 = 408 in²

    0
    2021-11-24T00:03:42+00:00

    Answer:

    Area of the square base: 144 in²

    Area of each triangular face: 66 in²

    Amount of paint needed: 408 in²

    Step-by-step explanation:

    We basically want to find the surface area of this square pyramid.

    First, find the areas of the 4 triangular sides. The area of a triangle is denoted by: A=\frac{1}{2} bh, where b is the base and h is the height.

    Here, the base coincides with the side length of the square, so b = 12. The height is 11, so h = 11. Plug these in:

    A=\frac{1}{2} bh

    A=\frac{1}{2} * 12 * 11 = 66 inches squared

    Each triangular face is thus 66 inches squared.

    Since there are 4 triangles, multiply 66 by 4: 66 * 4 = 264 inches squared

    Now, find the area of the square base. The area of a square is: A = s * s, where s is the side length. Here, the side length is 12, so s = 12. Plug this into the equation:

    A = s * s

    A = 12 * 12 = 144

    So, the square base is 144 inches squared.

    Finally, add 144 to 264 to get the total area Gabriel needs to paint:

    144 + 264 = 408 inches squared

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