$\Sigma M_D = 0$
$6R_A = 5(12) + 3(20)$
$R_A = 20 \, \text{ kN}$
$\Sigma M_A = 0$
$6R_D = 1(12) + 3(20)$
$R_D = 12 \, \text{ kN}$
At joint A
$\Sigma F_V = 0$
$\frac{\sqrt{21}}{5}F_{AG} = R_A$
$\frac{\sqrt{21}}{5}F_{AG} = 20$
$F_{AG} = 21.82 \, \text{ kN compression}$
$\Sigma F_H = 0$
$F_{AB} = \frac{2}{5}F_{AG}$
$F_{AB} = \frac{2}{5}(21.82)$
$F_{AB} = 8.73 \, \text{ kN tension}$
At joint G
$\Sigma F_V = 0$
$\frac{\sqrt{21}}{5}F_{BG} + 12 = \frac{\sqrt{21}}{5}F_{AG}$
$\frac{\sqrt{21}}{5}F_{BG} + 1 2 = \frac{\sqrt{21}}{5}(21.82)$
$F_{BG} = 8.73 \, \text{ kN tension}$
$\Sigma F_H = 0$
$F_{FG} = \frac{2}{5}F_{AG} + \frac{2}{5}F_{BG}$
$F_{FG} = \frac{2}{5}(21.82) + \frac{2}{5}(8.73)$
$F_{FG} = 12.22 \, \text{ kN compression}$
At joint B
$\Sigma F_V = 0$
$\frac{\sqrt{21}}{5}F_{BF} = \frac{\sqrt{21}}{5}F_{BG}$
$F_{BF} = F_{BG}$
$F_{BF} = 8.73 \, \text{ kN compression}$
$\Sigma F_H = 0$
$F_{BC} = F_{AB} + \frac{2}{5}F_{BG} + \frac{2}{5}F_{BF}$
$F_{BC} = 8.73 + \frac{2}{5}(8.73) + \frac{2}{5}(8.73)$
$F_{BC} = 15.71 \, \text{ kN tension}$
At joint F
$\Sigma F_V = 0$
$\frac{\sqrt{21}}{5}F_{CF} + \frac{\sqrt{21}}{5}F_{BF} = 20$
$\frac{\sqrt{21}}{5}F_{CF} + \frac{\sqrt{21}}{5}(8.73) = 20$
$F_{CF} = 13.09 \, \text{ kN compression}$
$\Sigma F_H = 0$
$F_{EF} + \frac{2}{5}F_{CF} = \frac{2}{5}F_{BF} + F_{FG}$
$F_{EF} + \frac{2}{5}(13.09) = \frac{2}{5}(8.73) + 12.22$
$F_{EF} = 10.48 \, \text{ kN compression}$
At joint C
$\Sigma F_V = 0$
$\frac{\sqrt{21}}{5}F_{CE} = \frac{\sqrt{21}}{5}F_{CF}$
$F_{CE} = F_{CF}$
$F_{CE} = 13.09 \, \text{ kN tension}$
$\Sigma F_H = 0$
$F_{CD} + \frac{2}{5}F_{CE} + \frac{2}{5}F_{CF} = F_{BC}$
$F_{CD} + \frac{2}{5}(13.09) + \frac{2}{5}(13.09) = 15.71$
$F_{CD} = 5.24 \, \text{ kN tension}$
At joint E
$\Sigma F_V = 0$
$\frac{\sqrt{21}}{5}F_{DE} = \frac{\sqrt{21}}{5}F_{CE}$
$F_{DE} = F_{CE}$
$F_{DE} = 13.09 \, \text{ kN compression}$
$\Sigma F_H = 0$
$F_{EF} = \frac{2}{5}F_{CE} + \frac{2}{5}F_{DE}$
$10.48 = \frac{2}{5}(13.09) + \frac{2}{5}(13.09)$
$10.5 = 10.5$ check
At joint D
$\Sigma F_V = 0$
$R_D = \frac{\sqrt{21}}{5}F_{DE}$
$12 = \frac{\sqrt{21}}{5}(13.09)$
$12 = 12$ check
$\Sigma F_{H} = 0$
$F_{CD} = \frac{2}{5}F_{DE}$
$5.24 = \frac{2}{5}(13.09)$
$5.24 = 5.24$ check
Summary
FAB = 8.73 kN tension
FAG = 21.82 kN compression
FBC = 15.71 kN tension
FBF = 8.73 kN compression
FBG = 8.73 kN tension
FCD = 5.24 kN tension
FCE = 13.09 kN tension
FCF = 13.09 kN compression
FDE = 13.09 kN compression
FEF = 10.48 kN compression
FFG = 12.22 kN compression