The area covered by the roof panel is 124 Inches. The area covered by the Side= 192 Inches, and The area covered by the ends = 72 inches. The total area of all the panels = 316 inches.
How were the figures above arrived at?
The calculations above were done using rudimentary mathematical concepts of the Area of a polygon and the Area of a triangle.
The Area of a polygon is given as: L X B.
The Area of a Triangle is given as 1/2 B * H.
A) For example, we know that the L of one panel of one side is 6' while it's breath is 8'. Hence the total area of all the four sides will be:
(8 * 6) x 4 = 192 inches.
B) The total panes on the roof are comprised of two triangles on both sides and two panels.
The information about the triangle is as follows:
Base = 8'
Height = 3'
Thus it's area = 1/2 * 8 * 3 = 12'. Hence the two triangular panels on each side will have a total area of 24inches.
How about the panels on the roof?
We have the length of each panel as 10 inches but the breath is unknown.
However, we can use the information about the triangles to solve this because the breath of the roof's panels forms the hypothenus of the triangles.
C - Lets us divide the triangle into two equal right-angled triangles. Such that:
Base = 4 inches
Height = 3 inches.
Hypothenuse = √(4²+3²)
= √(16+9)
= √25
= 5 inches.
Hence the roof panel sides are:
Length = 10 inches; and
Breath = 5 inches.
Thus the area of the rectangular roofing panels = (10 * 5) x 2 = 100inches.
Therefore the total area of the roofing (that is the rectangular panels and the triangular panels on both sides) equals
100 + 24 = 124 Inches.
Thus total area = 124 + 192 = 316 inches.
Learn more about Polygons and Triangles at:
https://brainly.com/question/1592456
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