in the given figure find the area of shaded region if AC is the diameter of semicircle on AC and BC is the radius of quadrant and BC=21& BD = 28
Answers
Answer:
428.6 cm²
Step-by-step explanation:
Since in the given figure, our aim tis to find the area of shaded region if AC is the diameter of semicircle on AC and BC is the radius of quadrant and BC=21& BD = 28.
The area of the shaded region is equal to the Area of Semi-circle plus the Area of triangle ABC minus the Area of quarter circle.
Thus:
Area of triangle = 1/2 x 21 x 28 = 294 cm²
Then in order to find area of semi-circle, we need to compute:
AC² = 28² + 21²
= 1225
⇒ AC = 35
The radius of semi-circle is equal to 35/2 = 17.5
Then, we can conclude that the Area is equal to
1/2 x 3.14 x (17.5)² = 480.8 cm²
Thus the Area of quarter circle is equal to:
1/4 x 3.14 x 21²= 346.2 cm²
Area of shaded region = 294 + 480.8 - 346.2 = 428.6 cm²
Hence, our area is equal to 428.6 cm².
Answer:
Area of shaded Region = 428.75 cm²
Step-by-step explanation:
in the given figure find the area of shaded region if AC is the diameter of semicircle on AC and BC is the radius of quadrant and BC=21& BD = 28
Area of Shaded region = Total Area - Arc area
Total Area = Area of Semi circle + Area of Triangle
Area of Triangle = (1/2) * Base * Height = (1/2) * 21 * 28 = 294 cm²
To find Area of Semi Circle , first we need to find radius
Radius = Diameter/2
Diameter is hypotenuse of triangle so using Pythagoras theorem
Diameter² = Base² + height²
=> Diameter² = 21² + 28²
=> Diameter² = 441 + 784
=> Diameter² = 1225
=> Diameter = 35 cm
Radius = 35/2
Are of Semi circle = (1/2) (22/7) (35/2)² = 11 * 5 * 35 / 4 = 481.25 cm²
Total Area = Area of Semicircle + Area Of Triangle
=> Total area = 481.25 + 294 = 775.25 cm²
Angle of arc = 90° Radius = 21 cm
Area of Arc = (90/360) (22/7) × 21² = 11 * 3 * 21 / 2 = 346.5 cm²
Area of Shaded region = 775.25 - 346.5 = 428.75 cm²
Area of shaded Region = 428.75 cm²