Question

XYZ is an equilateral triangle wil
angle with side 10 cm. If OP=3 cm, find the area of the shaded region correct to decimal places.
​

Answer 1

Area of the shaded region is $5(5\sqrt{3}-3 )$.

Step-by-step explanation:

Given:

Here, XYZ is an equilateral triangle.

So, XY =YZ = XZ =10 cm

Now,

Area of Δ XYZ = $\frac{\sqrt{3} }{4} \times (side)^2$

                        = $\frac{\sqrt{3} }{4} \times (10)^2$

                        = $\frac{\sqrt{3} }{4} \times 100$

                        = $\sqrt{3}\times 25$

                        = $25\sqrt{3} cm^2$

As shon in the figure, in Δ OYZ

we have, base = YZ = 10 cm and height = OP = 3 cm

Now,

Area of Δ OYZ = $\frac{1}{2}\times base \times height$

                         = $\frac{1}{2}\times YZ \times OP$

                         = $\frac{1}{2}\times 10 \times 3$

                         = $5\times 3$

                        = $15 cm^2$

So,

Area of the shaded region = Area of Δ XYZ - Area of Δ OYZ

                                              = $25\sqrt{3} - 15$

                                             = $5(5\sqrt{3}-3 )$

                 

Answer 2

Answer:

ANSWER IS 150 BUT I DON'T KNOW HOW.