Question

Here is a solid square-based pyramid.
The base of the pyramid is a square of side 12cm.
The height of the pyramid is 8cm.
X is the midpoint of QR and XT = 10cm.
A) Draw the front elevation of the pyramid from the direction of the arrow. Use a scale of 1 square to 1cm.
B) Work out the total surface area of the pyramid.

Answer 1

Answer:

Step-by-step explanation:

A. The front elevation of the pyramid in the direction of the arrow is herewith attached to this answer.

B. Base of the pyramid is a square of side 12 cm.

   The height of the pyramid is 8 cm.

   Slant height, XT, is 10 cm.

The total surface area of the pyramid can be determined by adding the surface areas that make up the shape.

Area of the triangular face = $\frac{1}{2}$ × base × slant height

                                            =  $\frac{1}{2}$ × 12 × 10

                                            = 60 $cm^{2}$

Area of the square base = length × length

                                         = 12 × 12

                                         = 144  $cm^{2}$

Total surface area of the pyramid = area of the base + 4 (area of the triangular face)

                              = 144 + 4(60)

                              = 144 + 240

                              = 384 $cm^{2}$

Therefore, total surface area of the pyramid is 384 $cm^{2}$.