find the l (lateral area) and the t (surface area) for the prism below.

$l = 2,730\text{ in}^2$ and $t = 3,150\text{ in}^2$
$l = 1,030\text{ in}^2$ and $t = 1,470\text{ in}^2$
$l = 1,030\text{ in}^2$ and $t = 1,250\text{ in}^2$
$l = 2,940\text{ in}^2$ and $t = 3,160\text{ in}^2$

Question

find the l (lateral area) and the t (surface area) for the prism below.

$l = 2,730\text{ in}^2$ and $t = 3,150\text{ in}^2$
$l = 1,030\text{ in}^2$ and $t = 1,470\text{ in}^2$
$l = 1,030\text{ in}^2$ and $t = 1,250\text{ in}^2$
$l = 2,940\text{ in}^2$ and $t = 3,160\text{ in}^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem", "Surface Area of a Prism", "Lateral Area of a Prism" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Surface Area of a Prism", "Lateral Area of a Prism" ] } ## Find the missing side of the triangular base $$ \begin{aligned} c &= \sqrt{20^2 + 21^2} \ c &= \sqrt{400 + 441} \ c &= \sqrt{841} = 29\text{ in} \end{aligned} $$ ## Calculate the lateral area of the prism $$ \begin{aligned} P &= 20 + 21 + 29 = 70\text{ in} \ h &= 39\text{ in} \ L &= P \cdot h = 70 \cdot 39 = 2,730\text{ in}^2 \end{aligned} $$ ## Calculate the total surface area of the prism $$ \begin{aligned} B &= \frac{1}{2} \cdot 20 \cdot 21 = 210\text{ in}^2 \ T &= L + 2B = 2,730 + 2(210) = 3,150\text{ in}^2 \end{aligned} $$

(A) L = 2,730 in² and T = 3,150 in²

(B) L = 1,030 in² and T = 1,470 in²

(C) L = 1,030 in² and T = 1,250 in²

(D) L = 2,940 in² and T = 3,160 in²

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Surface Area of a Prism" ] }

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QUESTION IMAGE

Question

Explanation:

Find the missing side of the triangular base

Calculate the lateral area of the prism

Calculate the total surface area of the prism

Answer: