The radius of the circle is 4 cm and the measure of the central angle is 90°.

The area of the sector with a central angle measuring 90° and radius of length 4 cm is π cm2.

The triangle in the sector is .

The area of the triangle is cm2.

The area of the segment of the circle is
(4π − ) cm2.

ii) In the triangle, the two sides are equal in measure, because the two sides represents the radius of the circle. The radius are the same in measure in a circle.

Therefore, the triangle is the second is an isosceles triangle.

iii) Area of a right triangle = [tex]\frac{1}{2} *base*height[/tex]

Here base = 4 and height = 4, plug in these values in the triangle formula, we get

The area of the triangle = [tex]\frac{1}{2} *4*4\\= 2*4\\= 8 cm^2[/tex]

iv) The area of the segment of the circle is (4π - area of the triangle).

= [tex](4\pi - 8)cm^2[/tex]

MrRoyal MrRoyal · Answer 2 · 2022-01-21T15:54:17+01:00

(a) Area of a sector

The area of a sector is calculated using:

[tex]A = \frac{\theta}{360} \times \pi r^2[/tex]

So, we have:

[tex]A = \frac{90}{360} \times \pi \times 4^2[/tex]

[tex]A = \frac{1}{4} \times \pi \times 4^2[/tex]

[tex]A = 4\pi[/tex]

Hence, the area of the sector is [tex]4\pi[/tex]

(b) The triangle

One of the angles in the triangle is 90 degrees.

So, the triangle is a right-angled triangle

The area of the triangle is then calculated as:

[tex]A = \frac 12 bh[/tex]

This gives

[tex]A = \frac 12 \times 4 \times 4[/tex]

[tex]A = 8[/tex]

Hence, the area of the triangle is 8, and the triangle is a right triangle

(c) The area of the segment of the circle

This is the difference between the areas of the circle and the triangle.

So, we have:

[tex]A = 4\pi - 8[/tex]

Hence, the area of the segment is [tex] 4\pi - 8[/tex]

The radius of the circle is 4 cm and the measure of the central angle is 90°. The area of the sector with a central angle measuring 90° and radius of length 4 cm is π cm2. The triangle in the sector is . The area of the triangle is cm2. The area of the segment of the circle is (4π − ) cm2.

Respuesta :

(a) Area of a sector

(b) The triangle

(c) The area of the segment of the circle

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