Given the figure below, calculate its area.

1+√3

Step-by-step explanation:

Area of the triangle = 1/2 * base * height

Area of the triangle = 1/2 * AC * BD

We need to get AC

AC = AD+DC

Get base AD using SOH CAH TOA

tan 45 = 4/AD

AD = 4/tan45

AD = 4/1

AD = 4

Get DC

tan 30 = 4/DC

DC = 4/tan 30

DC = 4/(1/√3)

DC = 4√3

AC = 4 + 4√3

AC = 4(1+√3)

Get the Area of the triangle

Area = 1/2 * 4 *  4(1+√3)

Area of the triangle = 1+√3