Diketahui bangun persegi ABCD memiliki panjang diagonal AC = 12√2 cm dan ∠BAC = 45°. Maka luas bangun persegi ABCD tersebut adalah....
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- Menentukan Luas Persegi Panjang ABCD
[tex]L = \frac{1}{2} \times {d}^{2} [/tex]
[tex]L = \frac{1}{2} \times (12\sqrt{2} × 12\sqrt{2} )[/tex]
[tex]L = \frac{1}{\cancel{2}} \times (\cancel{12}\sqrt{2} × 12\sqrt{2})[/tex]
[tex]L = 6 \sqrt{2} × 12\sqrt{2}[/tex]
[tex]L = (6 × 12) × ( \sqrt{2×2})[/tex]
[tex]L = 72 × \sqrt{4}[/tex]
[tex]L = 72 × 2[/tex]
[tex]L = 144 cm^{2}[/tex]
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Luas
= ½ × AC × AC
= ½ × 12√2 × 12√2
= 6√2 × 12√2
= 72 × 2
= 144 cm²
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