Geometry question: abcd and efgh are squares. if jh = 4 cm and jc = 9 cm, then what is the area of the shaded region?

Area of the shaded region is 130 cm².

Step-by-step explanation:

We can find the area of the shaded region of the square by subtracting area of smaller square from the bigger one.

JH = 4 cm and JC = 9 cm are the measurements.

Now we find one side of the smaller square.

Since HF²= EF² + EH²

(2×JH)² = EF² + EF² [Since HF = 2× JH and EF = EH]

(8)² = 2×EF²

EF² = 32

Now area of smaller square = EF² = 32 cm²

Similarly for bigger square

AC² = AB² + BC²

(2×JC)² = AB² + BC²

18² = 2×AB² (Since AB = BC)

AB² = 324/2 = 162

Area of Bigger square = AB² = 162 cm²

Now area of the shaded part = 162 - 32 = 130 cm²

Therefore area of the shaded area will be = 130 cm²