Answer:
30 square cm
Step-by-step explanation:
Key skills needed are: Triangle similarity, multiplication, proportions, subtraction
1) We first find that Triangle BCD is similar to triangle ACE. This is because they both have 1 right angle, and both share Angle BCD. Therefore, the other two angles are also the same measure.
2) Based on the statement above, 6/9 = 8/CE (CE just means the length of CE)
3) Solve this by cross multiplying -
[tex] \frac{6}{9} = \frac{8}{ce} [/tex]
This means that 6(CE) = 8(9)
4) Multiply it out: 6(CE) = 72
5) Divide by 6 and get CE = 12 cm.
6) Then use base time height to find the area of both triangles.
7) For triangle BCD: 6(8)/2 = 6(4) = 24 square centimeters
8) For Triangle ACE: 9(12)/2 = 9(6) = 54 square cm
9) To find the area of ABDE, you would subtract the are of triangle ACE by the area of triangle BCD
10) This is 54 - 24 = 30 square cm.
Hope you understood and have a nice day!! :D
