The value of the height of the prism is 8.68 inches
The surface area is the sum of the area of the faces.
The formula for calculating the surface area of the pyramid is;
TSA = [tex]a^2+2a\sqrt{\frac{a^2}{4} + h^2}[/tex]
where
a is the side length. = 7in
h is the height
Substitute
[tex]189=7^2+2(7)\sqrt{\frac{7^2}{2} + h^2} \\189=49+14\sqrt{\frac{49}{2} + h^2}\\140=14\sqrt{\frac{49}{2} + h^2}\\10=\sqrt{\frac{49}{2} + h^2}\\[/tex]
Square both sides to have
100 = 49/2 + h²
h² = 100 - 49/2
h² = 151/2
h² = 75.5
h = 8.68in
Hence the value of the height of the prism is 8.68 inches
Learn more on surface area here; https://brainly.com/question/1297098
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