Question

A square OABC is inscribed in a quadrant OPBQ a circle.if OA= 15 cm,find the area of the shaded region.

Answer 1

my answer cane out to be 128. something cm²

Answer 2

Answer:

Area of the shaded region $A== 252\text{ cm}^{2}$

Step-by-step explanation:

Given The side of the square OABC = 21 cm

In $\Delta OAB,\text{ }OA=AB\text{ side of the square}$

$OB^{2} = OA^{2}+AB^{2}\\\\\Rightarrow{OB}=21^{2}+21^{2}\\\\\Rightarrow{OB}=441+441\\\\\Rightarrow{OB}=882\\\\\Rightarrow{OB}=21\sqrt{2}$

Now, the radius of the circle is $OB=21\sqrt{2}$

Area of quadrant

$A_{2}=\frac{90^{\circ}}{360^{\circ}}\times\frac{22}{7}\times(21\sqrt{2})^{2}\\\\\Rightarrow{A}_{1}=\frac{1}{4}\times\frac{22}{7}\times882=693$

Area of the quadrant $A_{1}== 693\text{ cm}^{2}$

Now, area of the square OABC

$A_{2}=21\times21=441$

Therefore the area of the square  $A_{2}=441\text{ cm}^{2}$

therefore,

Area of the shaded region = area of quadrant - area of square 

$A=A_{1}-A_{2}=693-441=252$

Area of the shaded region $A=252\text{ cm}^{2}$