Question

The following picture is a square pyramid where AE=6√2 cm and ∠EAB=45°.

Find the surface area of the pyramid. (Make sure you include formulas and numbers in the formulas as part of your solution. Also include units in your final answer)

Answer 1

.

Explanation:

Answer 2

`288\ cm^2`

Explanation:

Consider the triangle AEB. This is isosceles triangle, because AE=EB. Thus, adjacent to the base AB angles are congruent, ∠EAB=∠EBA=45°. So, ∠AEB=180°-45°-45°=90°. We get the right isosceles triangle AEB, in which AE=6√2 cm. By the Pythagorean theorem,

`AB^2 =AE^2 +EB^2,\\ \\AB^2=(6√(2))^2+(6√(2))^2,\\ \\AB^2=72+72=144,\\ \\AB=12\ cm.`

The height to the base of the isosceles triangle is the median, the median to the hypotenuse in right triangle is half of the hypotenuse, so the height is 6 cm. The surface area of the pyramid consists of 4 side's area and the area of the base square. Hence,

`SA=4\cdot (1)/(2)\cdot 12\cdot 6+12\cdot 12=144+144=288\ cm^2.`