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If A B C D is a square with area 625
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02 Jun 2026, 13:50
02 Jun 2026, 13:50
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Question Stats:
71% (03:21) correct
28% (01:58) wrong based on 7 sessions
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If A B C D is a square with area 625 , and C E F D is a rhombus with area 500, then the area of the shaded region is
Note: Figure not drawn to scale
GRE ABCD.png [ 59.49 KiB | Viewed 447 times ]
\(
\begin{aligned}
& A. 125 \\
& B. 175 \\
& C. 200 \\
& D. 250 \\
& E. 275
\end{aligned}\)
Note: Figure not drawn to scale
Attachment:
GRE ABCD.png [ 59.49 KiB | Viewed 447 times ]
\(
\begin{aligned}
& A. 125 \\
& B. 175 \\
& C. 200 \\
& D. 250 \\
& E. 275
\end{aligned}\)
Re: If A B C D is a square with area 625
[#permalink]
30 Jun 2026, 12:15
30 Jun 2026, 12:15
Expert Reply
1. Find the Dimensions of the Square
- Area of Square A B C D=625
- Since it is a square, the side length is:
\(\text { Side }=\sqrt{625}=25\)
- This means the base C D=25 and the total vertical height of the square is 25 .
2. Find the Height of the Rhombus
- Area of Rhombus C E F D=500
- The rhombus shares the base C D with the square, so its base is also 25 .
- Using the area formula for a rhombus (Area $=$ base × height):
\(500=25 \times \text { height }\)
\(\text { height }=20\)
3. Calculate the Shaded Area
The shaded region inside the square can be split into two straightforward geometric shapes:
1. The Top Rectangle:
- Located above the rhombus line $E F$, extending to the top of the square A B .
- Width = 25 (the full width of the square)
- Height =25-20=5
\(\text { Area }_{\text {rectangle }}=25 \times 5=125\)
2. The Left Triangle:
- Located to the left of the rhombus leg C E .
- It is a right triangle with a vertical height of 20 .
- To find its horizontal base, we use the Pythagorean theorem on the rhombus side C E (which has a length of 25 ):
\(\begin{gathered}
\text { base }=\sqrt{25^2-20^2}=\sqrt{625-400}=\sqrt{225}=15 \\
\text { Area }_{\text {triangle }}=\frac{1}{2} \times 15 \times 20=150
\end{gathered}\)
Total Shading
Total Shaded Area \(=125+150=275\)
Correct Answer: E. 275
- Area of Square A B C D=625
- Since it is a square, the side length is:
\(\text { Side }=\sqrt{625}=25\)
- This means the base C D=25 and the total vertical height of the square is 25 .
2. Find the Height of the Rhombus
- Area of Rhombus C E F D=500
- The rhombus shares the base C D with the square, so its base is also 25 .
- Using the area formula for a rhombus (Area $=$ base × height):
\(500=25 \times \text { height }\)
\(\text { height }=20\)
3. Calculate the Shaded Area
The shaded region inside the square can be split into two straightforward geometric shapes:
1. The Top Rectangle:
- Located above the rhombus line $E F$, extending to the top of the square A B .
- Width = 25 (the full width of the square)
- Height =25-20=5
\(\text { Area }_{\text {rectangle }}=25 \times 5=125\)
2. The Left Triangle:
- Located to the left of the rhombus leg C E .
- It is a right triangle with a vertical height of 20 .
- To find its horizontal base, we use the Pythagorean theorem on the rhombus side C E (which has a length of 25 ):
\(\begin{gathered}
\text { base }=\sqrt{25^2-20^2}=\sqrt{625-400}=\sqrt{225}=15 \\
\text { Area }_{\text {triangle }}=\frac{1}{2} \times 15 \times 20=150
\end{gathered}\)
Total Shading
Total Shaded Area \(=125+150=275\)
Correct Answer: E. 275
gmatclubot
Re: If A B C D is a square with area 625 [#permalink]
30 Jun 2026, 12:15
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