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Sides 
of square ABCD are broken up by points W, X, Y, and Z as shown below. If 
6 inches long, what is the area, in square inches, of the shaded region?
of square ABCD are broken up by points W, X, Y, and Z as shown below. If 6 inches long, what is the area, in square inches, of the shaded region?- a)36
- b)32
- c)20
- d)16
- e)12
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Sides of square ABCD are broken up by points W, X, Y, and Z as shown b...
When square ABCD is divided as shown, each of the small triangles has legs of length 2 and 4. They also happen to be right triangles, because each shares one angle with the corner of the large square, which are right angles. To solve for the area of the shaded region, you can use the Pythagorean Theorem to calculate the length of the side of the shaded square.
Alternatively, you can find the area of one triangle, quadruple that value, and subtract it from the area of square ABCD, which is 62, or 36 square inches.
The area of a triangle is equal to 1/2 (base)(height). In a right triangle, either leg will work as the value for the base or the height, so the area of one triangle is A = 1/2 (2)(4) = 4. The area of the 4 triangles together, then, is 4 × 4, or 16. Thus the area of the shaded region is 36 − 16, or 20.
Alternatively, you can find the area of one triangle, quadruple that value, and subtract it from the area of square ABCD, which is 62, or 36 square inches.
The area of a triangle is equal to 1/2 (base)(height). In a right triangle, either leg will work as the value for the base or the height, so the area of one triangle is A = 1/2 (2)(4) = 4. The area of the 4 triangles together, then, is 4 × 4, or 16. Thus the area of the shaded region is 36 − 16, or 20.
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Sides of square ABCD are broken up by points W, X, Y, and Z as shown below. If 6 inches long, what is the area, in square inches, of the shaded region?a)36b)32c)20d)16e)12Correct answer is option 'C'. Can you explain this answer?
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Sides of square ABCD are broken up by points W, X, Y, and Z as shown below. If 6 inches long, what is the area, in square inches, of the shaded region?a)36b)32c)20d)16e)12Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Sides of square ABCD are broken up by points W, X, Y, and Z as shown below. If 6 inches long, what is the area, in square inches, of the shaded region?a)36b)32c)20d)16e)12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sides of square ABCD are broken up by points W, X, Y, and Z as shown below. If 6 inches long, what is the area, in square inches, of the shaded region?a)36b)32c)20d)16e)12Correct answer is option 'C'. Can you explain this answer?.
Sides of square ABCD are broken up by points W, X, Y, and Z as shown below. If 6 inches long, what is the area, in square inches, of the shaded region?a)36b)32c)20d)16e)12Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Sides of square ABCD are broken up by points W, X, Y, and Z as shown below. If 6 inches long, what is the area, in square inches, of the shaded region?a)36b)32c)20d)16e)12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sides of square ABCD are broken up by points W, X, Y, and Z as shown below. If 6 inches long, what is the area, in square inches, of the shaded region?a)36b)32c)20d)16e)12Correct answer is option 'C'. Can you explain this answer?.
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