Calculate the area of whole diagram .

Question

In Diagram show PQR is a triangle and QRS is a quadrant of circle with centre Q .. The arc RS is 55 cm . Calculate the area of whole diagram .

Answer 1

arc RS=55cm so circumference of the circle=4×55=220cm=2πr, where r=radius.

r=220/(2π)=110/π cm.

Since we have no other information or dimensions (we need the height and base lengths of the triangle), we could assume PQR is equilateral, because PQR cannot be inside the quadrant else we would only need the area of the sector which is independent of the area of the triangle. (It could also be an isosceles right triangle with QR as the height or hypotenuse.) We'll just consider the equilateral triangle.

Area of equilateral triangle=¼s²√3. s=r, so the combined areas are:

¼πr²+¼r²√3=¼r²(π+√3) where r=110/π.

(π+√3)/4=1.2184 approx, so the area is 1.2184r²=1493.76cm² approx.