Question

A square base pyramid is shown below. find its surgace area. Round to the nearest tenth

Answer 1

Given data

Height = 16.8 ft

Slant height = 19.3 ft

First, you find the base of the right angle triangle in the daigram.

Opposite = 16.8 ft

Hypotenuse = 19.3 ft

Adjacent = b

`\begin{gathered} \text{Appy pythagorus theorem} \\ \text{Opp}^2+Adj^2=Hypotenuse^2 \\ 16.8^2+b^2=19.3^2 \\ 282.24+b^2\text{ = 372.49} \\ b^2=372.49\text{ - 282.24} \\ b^2\text{ = 90.25} \\ b\text{ = }\sqrt[\square]{90.25} \\ b\text{ = 9.5} \end{gathered}`

Next,

The side of the base of the pyramid = 2 x b

= 2 x 9.5

= 19

The square measure 19 ft

To find the surface area of the pyramid, sum the areas of the square base and the area of the four triangles.

Area of the square = 19 x 19 = 361

`\begin{gathered} \text{Area of the four triangles = }(1)/(2)\text{ base x height} \\ \text{ = 0.5 x 19 x 19.3} \\ \text{ = 183.35} \\ \text{Area of the four triangle = 4 x 183.35 = 733.4} \end{gathered}`

Toal surface area of the figure = 733.4 + 361

= 1094.4