A banner is made of a square and a semicircle. The square has side lengths of 26 inches. One side of the square is also the diameter of the semicircle. What is the total area of the banner? Use 3.14 for π.

Question
Solid Geometry
asked 2020-11-09
A banner is made of a square and a semicircle. The square has side lengths of 26 inches. One side of the square is also the diameter of the semicircle. What is the total area of the banner? Use 3.14 for π.

Answers (1)

2020-11-10
[Pic]
The total area of the banner is the sum of the areas of the square and the semicircle (half cricle)
The side length of the square is 26 inches and the radius of the semicircle is 13 inches (half of the dimeter) so:
A=Asquare+Asemicircle
\(\displaystyle{A}={\left({s}^{{2}}\right)}+{\left(\frac{{1}}{{2}}\right)}π{r}^{{2}}\)
\(\displaystyle{A}={26}^{{2}}+\frac{{1}}{{2}}{\left({3.14}\right)}{\left({13}\right)}^{{2}}\)
\(\displaystyle{A}={676}+{265.33}\)
A=941.33 square inches.
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