Question

1. in rectangle f g h k, f c = c h = 8.5 cm. what is the area of rectangle f g h k? 15 cm² 120 cm² 125.5 cm²

Explanation:

Step1: Find the length of the diagonal

Since \(FC = CH=8.5\mathrm{cm}\), the length of the diagonal \(FH = FC + CH=8.5 + 8.5=17\mathrm{cm}\).

Step2: Use the Pythagorean theorem to find the length of \(FK\)

In right - triangle \(FGK\), \(FG = 8\mathrm{cm}\), \(FH = 17\mathrm{cm}\). Let \(FK=x\). By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(a = FG\), \(b = FK\), \(c = FH\)), we have \(8^{2}+x^{2}=17^{2}\). Then \(x^{2}=17^{2}-8^{2}=(17 + 8)(17 - 8)=25\times9 = 225\), so \(x = 15\mathrm{cm}\).

Step3: Calculate the area of the rectangle

The area of rectangle \(A=\text{length}\times\text{width}\). Here, length \(FK = 15\mathrm{cm}\) and width \(FG = 8\mathrm{cm}\), so \(A=15\times8 = 120\mathrm{cm}^2\).

Answer:

\(120\mathrm{cm}^2\)