The shape alongside is one quarter of a circle with radius 14 cm. find ,

i) the length of Arc.AB
ii)the perimeter of the figure
iii) the area of figure
iv) the area of triangle AOB
v) the area of the shaded segment

i) arc = 1/4 of the perimeter of the circle

ii) 14 + 14 + the arc length of i)
iii) find the area of the circle, then take 1/4 of it
iv) it will be a right-angled triangle, just use the formula for area of triangle
v) can't see any shaded region.

धन्यबद।

Puja

Your answer is incorrect

To solve these questions, we will need to use some formulas and properties of circles. Let's go step by step:

i) The length of Arc.AB:
The circumference of a full circle is given by the formula C = 2πr, where r is the radius. Since the given shape is one quarter of a circle, the length of the arc AB would be one-fourth of the circumference of the full circle.

C = 2πr = 2π(14 cm) ≈ 87.9646 cm
Length of Arc.AB = 1/4 * 87.9646 cm ≈ 21.9912 cm

ii) The perimeter of the figure:
The perimeter of the figure is the sum of the lengths of all the sides. In this case, it includes the arc AB and the two straight sides OA and OB.

Perimeter = Length of Arc.AB + OA + OB
Perimeter = 21.9912 cm + 14 cm + 14 cm = 49.9912 cm ≈ 50 cm

iii) The area of the figure:
The area of the figure includes the area of the quarter circle and the triangle AOB. To calculate the area of the quarter circle, we use the formula A = πr²/4. The area of the triangle can be calculated using the formula A = 1/2 * base * height.

Area of the quarter circle = πr²/4 = (π * (14 cm)²)/4 ≈ 153.938 cm²

iv) The area of triangle AOB:
The triangle AOB is a right triangle. We can use the formula A = 1/2 * base * height, where the base is one of the sides with length OA or OB, and the height is the distance between the base and the opposite vertex.

Base = OA = OB = 14 cm
Height = AB

To find the height, we can use the Pythagorean theorem:
AB² = OA² - OB²
AB² = (14 cm)² - (14 cm)² = 0
AB = √0 = 0 cm

Therefore, the height of the triangle is 0 cm, and the area of the triangle is 1/2 * 14 cm * 0 cm = 0 cm².

v) The area of the shaded segment:
To find the area of the shaded segment, we subtract the area of the triangle AOB from the area of the quarter circle.

Area of shaded segment = Area of quarter circle - Area of triangle AOB
Area of shaded segment = 153.938 cm² - 0 cm² = 153.938 cm²

So, the answers are:
i) The length of Arc.AB is approximately 21.9912 cm.
ii) The perimeter of the figure is approximately 50 cm.
iii) The area of the figure is approximately 153.938 cm².
iv) The area of triangle AOB is 0 cm².
v) The area of the shaded segment is approximately 153.938 cm².