[tex]c)a = 9[/tex]
[tex]b = 12[/tex]
[tex]d = 25[/tex]
[tex]d = \sqrt{{a}^{2} + {b}^{2} + {c}^{2} }[/tex]
[tex]25 = \sqrt{ {9}^{2} + {12}^{2} + {c}^{2} } [/tex]
[tex]25 = \sqrt{81 + 144 + {c}^{2} } [/tex]
[tex]25 = \sqrt{225 + {c}^{2} } \: |( \: )^{2} [/tex]
[tex] {25}^{2} = 225 + {c}^{2} [/tex]
[tex]625 = 225 + {c}^{2} [/tex]
[tex] {c}^{2} = 625 - 225[/tex]
[tex] {c}^{2} = 400[/tex]
[tex]c = \sqrt{400} [/tex]
[tex]c = 20 \: cm[/tex]
[tex]A_{l} = 2(a + b) \times c[/tex]
[tex]A_{l} = 2(9 + 12) \times 20[/tex]
[tex]A_{l} = 2 \times 21 \times 20[/tex]
[tex]A_{l} = 840 \: {cm}^{2} [/tex]
[tex]A_{t} = A_{l} + 2A_{b}[/tex]
[tex]A_{b} = a \times b[/tex]
[tex]A_{b} = 9 \times 12[/tex]
[tex]A_{b}=108 \: {cm}^{2} [/tex]
[tex]A_{t} = 840 + 2 \times 108[/tex]
[tex]A_{t} = 840 + 216[/tex]
[tex]A_{t} = 1056 \: {cm}^{2} [/tex]
[tex]V = a \times b \times c[/tex]
[tex]V = 9 \times 12 \times 20[/tex]
[tex]V = 2160 \: {cm}^{3} [/tex]
[tex]d)b = 5 \: cm[/tex]
[tex]c = 20 \: cm[/tex]
[tex]d = 21 \: cm[/tex]
[tex]d = \sqrt{ {a}^{2} + {b}^{2} + {c}^{2} } [/tex]
[tex]21 = \sqrt{ {a}^{2} + {5}^{2} + {20}^{2} } [/tex]
[tex]21 = \sqrt{ {a}^{2} + 25 + 400 } [/tex]
[tex]21 = \sqrt{ {a}^{2} + 425} \: |( \: )^{2} [/tex]
[tex] {21}^{2} = {a}^{2} + 425[/tex]
[tex]441 = {a}^{2} + 425[/tex]
[tex] {a}^{2} = 441 - 425[/tex]
[tex] {a}^{2} = 16[/tex]
[tex]a = \sqrt{16} [/tex]
[tex]a = 4 \: cm[/tex]
[tex]A_{l} = 2(a + b) \times c[/tex]
[tex]A_{l} = 2(4 + 5) \times 20[/tex]
[tex]A_{l} = 2 \times 9 \times 20[/tex]
[tex]A_{l} = 360 \: {cm}^{2} [/tex]
[tex]A_{t} = A_{l} + 2A_{b}[/tex]
[tex]A_{b} = a \times b[/tex]
[tex]A_{b} = 4 \times 5[/tex]
[tex]A_{b} = 20 \: {cm}^{2} [/tex]
[tex]A_{t} = 360 + 2 \times 20[/tex]
[tex]A_{t} = 360 + 40[/tex]
[tex]A_{t} = 400 \: {cm}^{2} [/tex]
[tex]V = a \times b \times c[/tex]
[tex]V = 4 \times 5 \times 20[/tex]
[tex]V = 400 \: {cm}^{3} [/tex]
