Areas of Plane Figures: 63.0 & 96.0 | Need Help w/ 3 & 4

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In summary, the area of a trapezoid is 63.0 or 60 if rounded to the nearest tenth, and the area for a parallelogram is 96.0 or 100 if rounded to the nearest tenth. Need help with 3 and 4. I think for 3 i would add 6 and 8 as the vertical diagonal and the horizontal diagonal would be 5 . 6+8=14 so the area would =35(rounded to nearest tenth would be 40) am i correct? Number 4 is where i get completely lost.
  • #1
Etrujillo
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I think the answer to number 1 is 63.0 or 60 if rounded to the nearest tenth, and i think number 2 is. 96.0 or 100 if rounded to the nearest tenth. Need help with 3 and 4. I think for 3 i would add 6 and 8 as the vertical diagonal and the horizontal diagonal would be 5 . 6+8=14 so the area would =35(rounded to nearest tenth would be 40) am i correct? Number 4 is where i get completely lost.

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  • #2
1.) The area for a trapezoid is given by:

\(\displaystyle A=\frac{h}{2}(B+b)\)

Plugging in the given values, we find:

\(\displaystyle A=\frac{6\text{ m}}{2}(11+10)\text{ m}=63\text{ m}^2\approx60\text{ m}^2\quad\checkmark\)

2.) The area for a parallelogram is given by:

\(\displaystyle A=bh\)

Plugging in the given values, we find:

\(\displaystyle A=(12\text{ in})(8\text{ in})=96\text{ in}^2\approx100\text{ in}^2\quad\checkmark\)

3.) The area for a kite can be found from the product of its diagonals. We can see one is 10 cm in length, and we can use Pythagoras to get the other:

\(\displaystyle \sqrt{6^2-5^2}+\sqrt{8^2-5^2}=\sqrt{6}+\sqrt{39}\)

And so the area is:

\(\displaystyle A=(10\text{ cm})((\sqrt{6}+\sqrt{39})\text{ cm})=10(\sqrt{6}+\sqrt{39})\text{ cm}^2\approx90\text{ cm}^2\)

4.) We have a trapezoid, and we know the big base \(B\) and the little base \(b\), but we don't know the height \(h\). But, we can find it using Pythagoras. Consider the right triangle making up the left part of the diagram. We are given the hypotenuse, and the smaller leg must be half the difference between the big base and the little base. Can you continue to find the height?
 
  • #3
If i use a2 + b2 = c2
I get 8^+4^=80
80 would be the other leg?
Would this be considered a right triangle?
So one leg would =4 (10-16) and the other 80?
 
  • #4
I just noticed you are instructed to round to the nearest tenth, not ten. :)

To find the height you need to use:

\(\displaystyle 3^2+h^2=8^2\implies h=\sqrt{8^2-3^2}=\sqrt{55}\)

Now, just plug in the numbers into the formula I gave in 1.) (Smile)
 

Related to Areas of Plane Figures: 63.0 & 96.0 | Need Help w/ 3 & 4

1. What are the formulas for finding the area of a rectangle?

The formula for finding the area of a rectangle is length x width or base x height.

2. How do I find the area of a triangle?

The formula for finding the area of a triangle is 1/2 x base x height.

3. Can you explain how to find the area of a circle?

To find the area of a circle, you can use the formula A = πr², where A is the area and r is the radius of the circle. Plug in the value of the radius into the formula and solve for the area.

4. Is there a formula for finding the area of a parallelogram?

Yes, the formula for finding the area of a parallelogram is base x height, where the base and height are perpendicular to each other.

5. How do I find the area of irregular shapes?

To find the area of an irregular shape, you can break it down into smaller, more familiar shapes and add or subtract their areas. Alternatively, you can also use the method of counting squares, where you draw a grid over the shape and count the number of squares inside to estimate the area.

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