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705-805 (Hard)|   Geometry|      
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Bunuel
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A square with side length 5 has its corner at the center of a square w 16 Jun 2020, 11:11
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75% (hard)

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54% (02:42) correct 46% (02:36) wrong based on 69 sessions

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A square with side length 5 has its corner at the center of a square with side length 4. The two squares overlap, and the overlapping region has one side equal to 3 as shown in the diagram above. What is the area where the two squares overlap?

A. 3
B. 4
C. 5
D. 6
E. 7

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A square with side length 5 has its corner at the center of a square w 16 Jun 2020, 11:26
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Bunuel

A square with side length 5 has its corner at the center of a square with side length 4. The two squares overlap, and the overlapping region has one side equal to 3 as shown in the diagram above. What is the area where the two squares overlap?

A. 3
B. 4
C. 5
D. 6
E. 7

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Area of shaded region = 1/4* Area of square - x + x = 1/4 * 4*4 = 4

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A square with side length 5 has its corner at the center of a square w 16 Jun 2020, 21:40
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In the figure, there's a typo. Correction: CD = 3-1 = 2.

Area of triangle ABC + Area of trapezoid ACDE = 0.5 * 2 * 1 + 0.5 * (2+1) * 2 = 1 + 3 = 4
Ans: 4
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A square with side length 5 has its corner at the center of a square w 22 Jun 2020, 21:47
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Lipun


In the figure, there's a typo. Correction: CD = 3-1 = 2.

Area of triangle ABC + Area of trapezoid ACDE = 0.5 * 2 * 1 + 0.5 * (2+1) * 2 = 1 + 3 = 4
Ans: 4
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Hi,

Could you please tell how did you deduce DE=1

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A square with side length 5 has its corner at the center of a square w 23 Jun 2020, 04:47
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DrMudassir

Hi,

Could you please tell how did you deduce DE=1

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Hi DrMudassir,

Since vertex of the larger square is the center of the smaller square, therefore, the sides of the larger square will move equal distance across each corresponding side of the smaller square when rotated about the center.
Side AB has shifted a distance of BC = 1 on the side of the smaller square, so the side AE must also have shifted by a distance of 1 unit towards D.

Hope it helps!

Lipun
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A square with side length 5 has its corner at the center of a square w 10 Jul 2023, 05:54
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