# Area of Cross-Section

Algebra

### Area of Cross-Section

A cross-shaped piece of metal has two opposite arms 4 1/2" in length, and the other two 4" in length. The arms are 1/2" in thickness. Determine area of cross-section.

Unsure how to proceed.

Guest

Guest

### Re: Area of Cross-Section

Image attached.

A is the 4 /12".

B and C are the 4".

T is thickness.

Attachments
CROSS.jpg (38.82 KiB) Viewed 389 times
Guest

### Re: Area of Cross-Section

You have to sum the area of 2 pair of rectangles and the square in the middle.

The first pair of rectangles area is $2 \cdot 4\frac{1}{2} \cdot \frac12 = 4\frac{1}{2}$
The second pair of rectangles area is $2 \cdot 4 \cdot \frac12 = 4$

The area of the square in the middle is $\frac12 \cdot \frac12 = \frac14$

The sum of these 3 numbers is $8 \frac12 + \frac14 = 8\frac24+\frac14 = 8\frac34$

Guest

Is it clear?

Guest

### Re: Area of Cross-Section

Yes, it is clear. Thanks.

One question:

If I wanted to determine the weight, do I need do add another thickness or use the present dimensions?

Guest

### Re: Area of Cross-Section

You need thickness because in order to calculate weight you have to know the volume of the figure not its area.

Guest

Thanks again.

Guest