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ABCD and EFGH are square. If JH = 4 cm and JC = 9 cm, then what is the area of the shaded region?thank you ! :)

ABCD and EFGH are square. If JH = 4 cm and JC = 9 cm, then what is the area of the-example-1
User Jbmyid
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1 Answer

16 votes
16 votes

Answer:

Step-by-step explanation:

From the information given,

ABCD and EFGH are squares

JH = 4

JC = 9

The diagonals of a square are perpendicular and bisect each other.

Considering triangle JEH,

angle J = 90 degrees

EJ = JH = 4

Triangle JEH is a right triangle. We would find EH by applying the Pythagorean theorem which is expressed as

hypotenuse^2 = one leg^2 + other leg^2

hypotenuse = EH

one leg = EJ = 4

other leg = JH = 4

Thus,

EH^2 = 4^2 + 4^2 = 16 + 16 = 32

EH = √32

Recall,

Area of a square = length^2

Length of square EFGH = √32

Area of square EFGH = (√32)^2 = 32

Considering triangle JBC,

angle J = 90 degrees

JC = JB = 9

Triangle JBC is a right triangle. We would find BC by applying the Pythagorean theorem. From triangle JBC,

hypotenuse = BC

one leg = JC = 9

other leg = JB = 9

Thus,

BC^2 = 9^2 + 9^2 = 81 + 81 = 162

BC = √162

Length of square ABCD = √162

Area of square ABCD = (√162)^2 = 162

Area of shaded region = area of square ABCD - area of square EFGH = 162 - 32

Area of shaded region = 130 cm^2

User Chenna
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