The base of given triangle is 8 cm.
Further explanation:
The area of triangle is calculated by using two methods
- Hero's formula
- Base and Height
Hero's formula requires all three sides of triangle while we can use only base and height in second formula.
Given
![A = 20\ cm^2\\h = 5\ cm](https://tex.z-dn.net/?f=A%20%3D%2020%5C%20cm%5E2%5C%5Ch%20%3D%205%5C%20cm)
As the area of triangle and height are given, then
![A = 0.5*b*h\\20=0.5*b*5\\20=2.5b\\b=\frac{20}{2.5}\\b=8\ cm](https://tex.z-dn.net/?f=A%20%3D%200.5%2Ab%2Ah%5C%5C20%3D0.5%2Ab%2A5%5C%5C20%3D2.5b%5C%5Cb%3D%5Cfrac%7B20%7D%7B2.5%7D%5C%5Cb%3D8%5C%20cm)
The base of given triangle is 8 cm.
Keywords: Area of triangle, base, height
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#3. Plugging the point (3,0) into any of the equations except the third one gives an invalid answer.
Yes I think that it’s D because it makes more sense.
To find the total surface area of this cone, we have that the total lateral area is given by the formula:
![A_{\text{lateral}}=s\cdot\pi\cdot r](https://tex.z-dn.net/?f=A_%7B%5Ctext%7Blateral%7D%7D%3Ds%5Ccdot%5Cpi%5Ccdot%20r)
Where
s is the slant height of the cone, s = 12 inches.
r is the radius of the base of the cone, r = 7 inches.
To that area, we need to add the area of the base of the cone:
![A_{\text{base}}=\pi\cdot r^2](https://tex.z-dn.net/?f=A_%7B%5Ctext%7Bbase%7D%7D%3D%5Cpi%5Ccdot%20r%5E2)
That is, this is the area of a circle with this radius. Then, the total surface area is:
![A_{\text{total}=}s\cdot\pi\cdot r+\pi\cdot r^2](https://tex.z-dn.net/?f=A_%7B%5Ctext%7Btotal%7D%3D%7Ds%5Ccdot%5Cpi%5Ccdot%20r%2B%5Cpi%5Ccdot%20r%5E2)
Substituting the values in this formula, we have:
![A_{\text{total}}=12in\cdot3.14\cdot7in+\pi\cdot(7in)^2=263.76in^2_{}+153.86in^2](https://tex.z-dn.net/?f=A_%7B%5Ctext%7Btotal%7D%7D%3D12in%5Ccdot3.14%5Ccdot7in%2B%5Cpi%5Ccdot%287in%29%5E2%3D263.76in%5E2_%7B%7D%2B153.86in%5E2)
Then
![A_{\text{total}}=417.62in^2](https://tex.z-dn.net/?f=A_%7B%5Ctext%7Btotal%7D%7D%3D417.62in%5E2)
Hence, the total area is equal to 417.62 square inches.
Let's convert them to decimals:
1/25 = 0.04
4% = 0.04
0.04 = 0.04
0.4 = 0.40.
So 0.4 is NOT equivalent to the other values.