Răspuns:
[tex]\boldsymbol{ \red{D. \ 180 \ cm^2}}[/tex]
Explicație pas cu pas:
Apotemele bazelor sunt:
[tex]L = 12 \ cm \Rightarrow a_B = \dfrac{L}{2} = 6 \ cm[/tex]
[tex]\ell = 6 \ cm \Rightarrow a_b = \dfrac{\ell}{2} = 3 \ cm[/tex]
Apotema trunchiului:
[tex]\boxed{\boldsymbol{a_{t}^{2} = h^{2} + (a_{B} - a_{b})^{2} }}[/tex]
[tex]a_{t} = \sqrt{4^{2} + (6 - 3)^{2} } = \sqrt{16 + 9} = \sqrt{25} = 5 \ cm[/tex]
Aria laterală:
[tex]\boxed{\boldsymbol{\mathcal{A}_{\ell} = \dfrac{(\mathcal{P}_{B} + \mathcal{P}_{b}) \cdot a_{t}}{2}}}[/tex]
[tex]\mathcal{A}_{\ell} = \dfrac{(4 \cdot L + 4 \cdot \ell) \cdot a_{t}}{2} = \dfrac{4 \cdot (12 + 6) \cdot 5}{2} = 180 \ cm^2[/tex]
R: D. 180 cm²
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