Question

a piece of wire is bent in the shape of an equilateral triangle whose each side measures 8.8 CM . the same wire is Bent to form a circular ring .what is the diameter of the Ring? which shape encloses more area? ​

Answer 1

Answer:

Diameter of the ring = 8.4 cm

Area of the circle is greater than that of the triangle.

Step-by-step explanation:

As the perimeter of the circle and the triangle are the same because they are made from the same length of wire,

Perimeter of equilateral triangle = 3s

s = 8.8 cm

∴ 3s = 3 × 8.8 = 26.4 cm

Perimeter of a circle = πd = $\frac{22d}{7}=26.4$

$d=\frac{7*26.4}{22}=8.4$ cm.

∴ Diameter of the circle = 8.4 cm.

Area of the triangle = $\frac{a^2\sqrt{3}}{4} = \frac{8.8^2\sqrt{3}}{4}=\frac{8.8 *8.8\sqrt{3}}{4}={2.2 *8.8\sqrt{3}=19.36\sqrt{3}$

∴ Area of the triangle = 19.36$\sqrt{3}$ cm²

Let $\sqrt{3}$ = 1.732

∴ Area of the triangle = 19.36 × 1.732 = 33.53152 cm²

Area of a square = $\frac{\pi}{4}d^{2} = \frac{22}{28}\times8.4\times8.4=22\times1.2\times2.1=55.44$ cm²

Clearly, 33.5352 < 55.44

∴ Circle has more area.

Hope it helps...

Belated HAPPY NEW YEAR TOO!!!