Question

ABCD is square of side `4` cm. If E is point in the interior of the square such that `Delta CED` is equilateral, then find the area of `Delta ACE` in `cm^2`

Answer 1

Area of `Delta CED(A_1) = sqrt3/4**4**4 = 4sqrt3 cm^2`
Area of `Delta AED(A_2) = 1/2**AD**ED**sin /_ADE`
Here, `AD = DE = 4cm`
`/_ADE = 90^@-/_CDE = 90^@-60^@ = 30^@`
`:.` Area of `Delta AED(A_2) = 1/2**4**4**sin30^@ = 8**1/2 = 4cm^2`
Area of `Delta ADC(A_3) = 1/2**4**4 = 8cm^2`
`:.` Area of `Delta AEC(A) = A_1+A_2-A_3`
`=> A= 4sqrt3+4-8 = 4sqrt3-4 = 4(sqrt3-1)cm^2`
So, area of `Delta ACE` is `4(sqrt3-1)cm^2`.