The area of the unshaded region is 58.5 square units
From the question, the image shows a triangle inscribed in a circle of radius r. The triangle is completely shaded.
Therefore, the area of the unshaded part will be difference between the area of the circle and the area of the triangle.
Area of unshaded part = Area of circle - Area of triangle
Area of a circle is given by the formula
[tex]A =\pi r^{2}[/tex]
Where A is the area and r is the radius
Area of a triangle is given by the formula
[tex]A=\frac{1}{2}bh[/tex]
Where A is the Area, b is the base and h is the perpendicular height
∴ Area of the unshaded region = [tex]\pi r^{2} - \frac{1}{2} bh[/tex]
From the question
h = 4, b = 10, and r = 5
∴ Area of the unshaded region = [tex]\pi \times 5^{2} - \frac{1}{2} \times 10 \times 4[/tex]
Area of the unshaded region = 25π - 5×4
From the question π = 3.14
∴ Area of the unshaded region = 25×3.14 - 5×4
Area of the unshaded region = 78.5 - 20
Area of the unshaded region = 58.5 square units
Hence, the area of the unshaded region is 58.5 square units
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