Answer:
The area of the circle having diameter of 26 is 530.66 square units.
Explanation:
Given:
Diameter of the circle= 26 units
To find:
Area of the circle =?
Solution:
Finding area using Diameter
[tex]\text {Area } A=\pi\left(\frac{d}{2}\right)^{2}[/tex]
substituting the values we get,
[tex]\text {Area } A=3.14\left(\frac{26}{2}\right)^{2}[/tex]
[tex]\text {Area } A=3.14(13)^{2}[/tex]
[tex]\text {Area } A=3.14(169)[/tex]
[tex]\text {Area } a=530.66 \text { units }[/tex]
Following methods can also be used to find the area of the circle.
Aliter1: finding area using radius
[tex]\text {radius } r=\frac{\text {diamater}}{2}[/tex]
[tex]\text {radius } r=\frac{26}{2}[/tex]
[tex]\text {radius } r=13 \text {units}[/tex]
Now ,
[tex]\text {Area } A=\pi r^{2}[/tex]
[tex]\text {Area } A=(3.14)(13)^{2}[/tex]
[tex]\text {Area } A=(3.14)(169)[/tex]
[tex]\text {Area } A=530.66 \text { square units }[/tex]
Aliter 2:Finding Area using circumference
Circumference of the circle [tex]c=2 \pi r[/tex]
[tex]c=2 \times(3.14)(13)[/tex]
[tex]c=2 \times(40.82)[/tex]
[tex]c=81.64 \text { units }[/tex]
Now
\operatorname [tex]{Area} A=\frac{c^{2}}{4 \pi}[/tex]
Substituting values,
[tex]\text {Area } A=(81.64)^{2} /(4 \pi)[/tex]
[tex]\text {Area } A=(81.64)^{2} /(4)(3.14)[/tex]
[tex]\text {Area } A=(665.08) /(4)(3.14)[/tex]
[tex]\text { Area } A=(6665.08) /(12.56)[/tex]
[tex]\text { Area } A=530.66 \text { square units }[/tex]
Result:
Thus the area of the circle with a diameter 26 units is 530.66 square units.
