Question

The following picture is a square pyramid where DE=8 cm and m∠ADE=60°.

Answer 1

Given:

The length of DE is 8 cm and the measure of ∠ADE is 60°.

We need to determine the surface area of the pyramid.

Length of AD:

The length of AD is given by

$cos 60^{\circ}=\frac{FD}{8}$

       $4=FD$

Length of AD = 8 cm

Slant height:

The slant height EF can be determined using the trigonometric ratio.

Thus, we have;

     $sin \ 60^{\circ}=\frac{EF}{8}$

$sin \ 60^{\circ} \times 8=EF$

      $\frac{\sqrt{3}}{2} \times 8=EF$

          $4\sqrt{3}=EF$

Thus, the slant height EF is 4√3

Surface area of the square pyramid:

The surface area of the square pyramid can be determined using the formula,

$SA=Area \ of \ square + \frac{1}{2} (Perimeter \ of \ base ) (slant \ height)$

Substituting the values, we have;

$SA=8^2+\frac{1}{2}(8+8+8+8)(4 \sqrt{3})$

$SA=64+\frac{1}{2}(32)(4 \sqrt{3})$

$SA=64+(16)(4 \sqrt{3})$

$SA=64+64 \sqrt{3}$

The exact form of the area of the square pyramid is $64+64 \sqrt{3}$

Substituting √3 = 1.732 in the above expression, we have;

$SA = 64 + 110.848$

$SA = 174.848$

Rounding off to one decimal place, we get;

$SA = 174.8$

Thus, the area of the square pyramid is 174.8 cm²

Answer 2

Answer:

174.9 cm²

Step-by-step explanation:

AD = 2 × (8cos60)

AD = 8

Base = 8²

= 64

4 triangles = 4(½ × 8 × 8sin60)

= 64sqrt(3)

SA = 64 + 64sqrt(3)

174.8512517