Find the area of the shaded region in figure 5, if AC = 24 cm, BC = 10 cm and O is the centre of the circle. [Use π = 3.14]
Answers
Answer:
410.66 cm²
Step-by-step explanation:
Concept:
1.Angle in a semi circle is right angle.
2. Pythagoras theorem:
In a right angled triangle square on the hyopotenuse is equal to sum of the squares on the other two sides.
clearly triangle ABC is right angled triangle.
By pythagors theorem,
AB² = AC² + BC²
AB² = 24² + 10²
AB² = 576 + 100
AB² = 676
AB = 26 cm
That is, diameter of the circle = 26 cm
2r = 26
r = 13 cm
Area of the shaded region
=(Area of the semicircle) - (Area of the
ΔABC)
= π r² - (1/2) (BC)(AC)
= (3.14)(13×13) - (1/2) (10)(24)
= (3.14)(169) - (10)(12)
= 530.66 - 120
= 410.66 cm²
Answer:- Area of shaded region =145.33 cm square
Step-by-step explanation:
It is given that,
,AC=24cm BC=10cm and O is the center of the circle
To find AB
Triangle ABC is a right angled triangle.
AB = 26 cm
Diameter = 26 cm
r = 13 cm
To find the area of triangle ABC
Area of right angled triangle =
∴ Area of triangle , A₁ = 120 cm square
To find area of semicircle
Area of semi circle is given by
A₂= πr²/2
A₂= (3.14 x 13 x 13)/2 = 265.33
To find area of shaded region
Area of shaded region = A₂ - A₁ =265.33 - 120 = 145.33 cm square
Hope this helps you.