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Let's find the perimeter first by adding all the side lengths together. There are two missing side lengths, which we can find by taking the side opposite them and subtract the side behind the missing side from them.
I've attached a diagram showing how to find the side lengths.
Now let's add all the side lengths together: 4 cm + 8 cm + 8 cm + 2 cm + 4 cm + 6 cm = 32 cm
The perimeter of this figure is 32 cm.
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To find the area we can divide this figure into 2 rectangles. On the second attached diagram, I've split the figure into two and labeled the length and width of each rectangle.
Area of a rectangle = length * width
Area of red labeled rectangle = 4 cm * 2 cm = 8 cm²
Area of yellow labeled rectangle = 8 cm * 4 cm = 32 cm²
Add the two areas together: 8 + 32 = 40
The area of the figure is 40 cm².
Answer: the system has no solution.
Step-by-step explanation:
\displaystyle\\
\left \{ {{x^2y=16\ \ \ \ \ (1)} \atop {x^2+4y+16=0\ \ \ \ \ (2)}} \right. .\\
Multiply\ both\ sides\ of\ the\ equation\ (2)\ by\ y\ (y\neq 0):\\
x^2y+4y^2+16y=0\\
We\ substitute\ equation\ (1)\ into\ equation\ (2):\\
16+4y^2+16y=0\\
4y^2+16y+16=0\\
4*(y^2+4y+4)=0\\
4*(y^2+2*y*2+2^2)=0\\
4*(y+2)^2=0\\
Divide\ both\ sides\ of\ the \ equation\ by\ 4:\\
(y+2)^2=0\\
(y+2)*(y+2)=0\\
So,\ y+2=0\\
y=-2.\\