Question 1103454
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The side of the base is 12; so the distance across the base from one side to the other is 12; so the distance from the middle of one side of the base to the center of the base is 6.<br>
Then with a slant height of 15, the height of the pyramid is the other leg of a right triangle with hypotenuse 15 and one leg 6:
{{{sqrt(15^2-6^2) = sqrt(225-36) = sqrt(189) = 3*sqrt(21)}}}<br>
Answer a: {{{3*sqrt(21)}}} (cm)<br>
The volume of the pyramid is {{{(1/3)Bh = (1/3)(144)(3*sqrt(21)) = 144*sqrt(21)}}}
Answer b: {{{144*sqrt(21)}}} (cubic cm)<br>
The area of the base is 144; the area of each triangular face is {{{(1/2)bh = (1/2)(12)(15) = 90}}}
The total surface area is {{{144+4(90) = 144+360 = 504}}}  (square cm)