bantu dijawab kk beserta gambar bangunnya janji jadikan jawaban terbaik

Mapel : Matematika
Materi : Bangun Datar - Garis Tinggi Segitiga

Pertanyaan 1
Diketahui :
rusuk kubus ABCD.EFGH (a) = 6 cm

Ditanya :
Jarak A - HB

Jawab :
[tex]\text{Mencari panjang HA (diagonal bidang kubus)}\\ \\HA=a \sqrt{2}=6 \sqrt{2}\ cm\\ \\\text{Mencari panjang HB (diagonal ruang kubus)}\\ \\HB=a \sqrt{3}=6\sqrt{3}\ cm\\ \\\text{Mencari Luas segitiga HAB }\\ \\L=\frac{1}{2}\times HA\times AB\\ \\L=\frac{1}{2}\times6\sqrt{2}\times6\\ \\L=18\sqrt{2}\ cm^2\\ \\\text{Mencari Garis Tinggi A-HB }\\ \\L=\frac{1}{2}\times HB \times (A-HB)\\ \\18\sqrt{2}=\frac{1}{2}\times6\sqrt{3}\times (A-HB)\\ \\(A-HB)=(\frac{18\sqrt{2}}{6\sqrt{3}})\times2[/tex]

[tex](A-HB)= \frac{6\sqrt{2}}{\sqrt{3}}\\ \\ (A-HB)=\frac{6\sqrt{2}}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\ \\ (A-HB)=\frac{6\sqrt{6}}{3}\\ \\ \bold{(A-HB)=2\sqrt{6}\ cm} \approx 4,9\ cm[/tex]


Pertanyaan 2
Diketahui :
rusuk kubus ABCD.EFGH (a) = 8 cm

Ditanya :
Jarak H - AC

Jawab :

[tex]\text{Mencari panjang HA dan AC (diagonal bidang kubus)}\\ \\HA=AC=a \sqrt{2}=8 \sqrt{2}\ cm \\ \\ \text{Mencari panjang H-AC (tinggi segitiga ACH)}\\ \\(H-AC)=\sqrt{(HA)^2-( \frac{1}{2}AC)^2}\\ \\(H-AC)=\sqrt{(8 \sqrt{2})^2-( 4 \sqrt{2})^2} \\ \\(H-AC)=\sqrt{(64\times2)-(16\times2)}\\ \\(H-AC)=\sqrt{(64-16)\times2}\\ \\(H-AC)=\sqrt{48\times2}\\ \\(H-AC)=\sqrt{96}\\ \\(H-AC)=\sqrt{16\times6}\\ \\\bold{(H-AC)=4 \sqrt{6}\ cm} \approx 9,8\ cm [/tex]

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