Square ABCD is inscribed in the sector A-PCQ. The radius of sector C-BXD is 20 cm. Complete the activity to find the area of the shaded region. (π = 3.14)

In the figure 7.48, square ABCD is inscribed in the sector A-PCQ. The radius of sector C-BXD is 20 cm. Complete the following activity to find the area of the shaded region. (\(\pi=3.14\))

Figure: A-PCQ is a quarter circle with centre A and radius AC; B lies on radius AP and D on radius AQ, C on the arc PQ. C-BXD is a quarter circle with centre C through B and D (X on its arc). Shaded: the part of the square outside sector C-BXD, and the two parts of sector A-PCQ outside the square.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

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Answer: Total shaded area = 86 + 228 = 314 cm²

Side of square = radius of sector C-BXD = 20 cm. Area of square \(=20^2=400\) cm².

Shaded region inside the square = A(□ABCD) − A(C-BXD):

\[400-\frac{90}{360}\times3.14\times400=400-314=86\]

Radius of bigger sector = diagonal AC \(=20\sqrt2\) cm.

Shaded regions outside the square = A(A-PCQ) − A(□ABCD):

\[\frac{90}{360}\times3.14\times(20\sqrt2)^2-400\]

\[=628-400=228\]

Total shaded area \(=86+228=314\) cm².

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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Square ABCD is inscribed in the sector A-PCQ. The radius of sector C-BXD is 20 cm. Complete the activity to find the area of the shaded region. (π = 3.14)

1 answer

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