Geometry help!! I don’t know how to do this

9514 1404 393

  659.52 cm^2

Step-by-step explanation:

In order to find the surface area of this figure, we need to know the dimensions of the base. If we assume the base is square, then the distance from its center to the center of one edge is half the dimension of one side of the base.

That center-to-edge distance (x) can be found from the given dimensions using the Pythagorean theorem.

  x^2 + (15.4 cm)^2 = (17 cm)^2

  x^2 = (289 -237.16) cm^2 = 51.84 cm^2

  x = √51.84 cm = 7.2 cm

This means the edge length of the prism base is 2×7.2 cm = 14.4 cm.

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The total surface area of the square prism is ...

  A = b^2 +2bs . . . where b is the edge length of the base, s is the slant height

  A = (14.4 cm)^2 + 2(14.4 cm)(17 cm) = 659.52 cm^2

The total surface area of this square pyramid is 659.52 cm^2.