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<u>Given</u>:
The length of DE is 8 cm and the measure of ∠ADE is 60°.
We need to determine the surface area of the pyramid.
<u>Length of AD:</u>
The length of AD is given by
Length of AD = 8 cm
<u>Slant height:</u>
The slant height EF can be determined using the trigonometric ratio.
Thus, we have;
Thus, the slant height EF is 4√3
<u>Surface area of the square pyramid:</u>
The surface area of the square pyramid can be determined using the formula,
Substituting the values, we have;
The exact form of the area of the square pyramid is
Substituting √3 = 1.732 in the above expression, we have;
Rounding off to one decimal place, we get;
Thus, the area of the square pyramid is 174.8 cm²