Question

Javier is constructing a door for his son's tree house. The dimensions of the rectangular door are 6a^2-a+2 feet and 3a^2+5 feet. He wants to cut out a square from the door to insert a glass panel, as per the diagram below. The glass panel will have a height of a -3 feet.After Javier removes the square for the glass panel, how much of the door will be made from wood?

Answer 1

The area of a figure is the amount of space the figure can occupy. $18a^4 + 10$ of the door will be made from the wood.

Given

$Length = 6a^2 + 2$

$Width = 3a^2 + 5$

First, calculate the area of the rectangular door

$Area = Length \times Width$

$Area =(6a^2 + 2) \times ( 3a^2 + 5)$

$Area = 18a^4 + 6a^2 + 30a^2 + 10$

$Area = 18a^4 + 36a^2 + 10$

Next, calculate the area of the glass panel

The dimension of the glass panel is not given, and the diagram is not attached. So, I will assume the dimension of the square glass panel is $6a$.

So, the area of the glass panel is:

$Area = 6a \times 6a$

$Area = 36a^2$

To calculate how much wood that will be needed for the rectangular door, we simply subtract the area of the glass panel from the area of the door

$Wood = 18a^4 + 36a^2 + 10 - 36a^2$

Collect like terms

$Wood = 18a^4 + 10 + 36a^2 - 36a^2$

$Wood = 18a^4 + 10$

Considering the assumed value, $18a^4 + 10$ of the door will be made from the wood.

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