Answer:
16 cm^2
Step-by-step explanation:
Given
-- Bigger Triangle
-- Smaller Triangle
--- Scale factor
Area of CBD = 9
Required
Determine the area of CAE
The area of triangle CBD is:
![A_1 = \frac{1}{2}bh](https://tex.z-dn.net/?f=A_1%20%3D%20%5Cfrac%7B1%7D%7B2%7Dbh)
![\frac{1}{2}bh = 9](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dbh%20%3D%209)
The area of CAE is:
![A_2 = \frac{1}{2}BH](https://tex.z-dn.net/?f=A_2%20%3D%20%5Cfrac%7B1%7D%7B2%7DBH)
Where:
and
![H = \frac{4}{3}h](https://tex.z-dn.net/?f=H%20%3D%20%5Cfrac%7B4%7D%7B3%7Dh)
The above values is the dimension of the larger triangle (after dilation).
So, we have:
![A_2 = \frac{1}{2}*\frac{4}{3}b * \frac{4}{3} * h](https://tex.z-dn.net/?f=A_2%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7B4%7D%7B3%7Db%20%2A%20%5Cfrac%7B4%7D%7B3%7D%20%2A%20h)
![A_2 = \frac{1}{2}*\frac{4}{3} * \frac{4}{3} *b* h](https://tex.z-dn.net/?f=A_2%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7B4%7D%7B3%7D%20%2A%20%5Cfrac%7B4%7D%7B3%7D%20%2Ab%2A%20h)
![A_2 = \frac{1}{2}*\frac{16}{9} *b* h](https://tex.z-dn.net/?f=A_2%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7B16%7D%7B9%7D%20%20%2Ab%2A%20h)
Re-order
![A_2 = \frac{16}{9}*\frac{1}{2}* b* h](https://tex.z-dn.net/?f=A_2%20%3D%20%5Cfrac%7B16%7D%7B9%7D%2A%5Cfrac%7B1%7D%7B2%7D%2A%20b%2A%20h)
![A_2 = \frac{16}{9}*\frac{1}{2}bh](https://tex.z-dn.net/?f=A_2%20%3D%20%5Cfrac%7B16%7D%7B9%7D%2A%5Cfrac%7B1%7D%7B2%7Dbh)
Recall that:
![\frac{1}{2}bh = 9](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dbh%20%3D%209)
![A_2 = \frac{16}{9}*9](https://tex.z-dn.net/?f=A_2%20%3D%20%5Cfrac%7B16%7D%7B9%7D%2A9)
![A_2 = 16](https://tex.z-dn.net/?f=A_2%20%3D%2016)
Hence, the area is 16 cm^2
Answer:your welcome
Step-by-step explanation:
Mhhh
The correct answer is 4x-10