Find the area of triangle.

Mathematics

1 answer:

kompoz [17]4 years ago

8 0

Look at the traingle upside down.

The base is 6 and the height is 5 (remember that height must be perpendicular to the base and that the red lines aren't actually a part of the figure).

6*5=30
30/2=15

Final answer: 15 yd^2

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About the $x$ -axis (washer method):

$\displaystyle\pi\int_2^5\left(6^2-\left(\frac43x-\frac23\right)^2\right)\,\mathrm dx=\frac{16\pi}9\int_2^5(20+x-x^2)\,\mathrm dx=\boxed{56\pi}$

About the $y$ -axis (shell method):

$\displaystyle2\pi\int_2^5x\left(6-\left(\frac43x-\frac23\right)\right)\,\mathrm dx=\frac{8\pi}3\int_2^5x(5-x)\,\mathrm dx=\boxed{36\pi}$

About $x=7$ (shell method):

$\displaystyle2\pi\int_2^5(7-x)\left(6-\left(\frac43x-\frac23\right)\right)\,\mathrm dx=\frac{8\pi}3\int_2^5(35-12x+x^2)\,\mathrm dx=\boxed{48\pi}$

About $y=2$ (washer method):

$\displaystyle\pi\int_2^5\left((6-2)^2-\left(\frac43x-\frac23-2\right)^2\right)\,\mathrm dx=\frac{16\pi}9\int_2^5(5+4x-x^2)\,\mathrm dx=\boxed{32\pi}$