Question

1. find the surface area of the prism. 5 cm 12 cm 13 cm 4 cm 120 cm² 333 cm² 180 cm²

Explanation:

Step1: Identify prism type

It's a triangular prism with triangular base sides 5cm, 12cm, 13cm (right triangle, since $5^2+12^2=13^2$) and length 4cm.

Step2: Calculate base area

Area of right triangle: $\frac{1}{2}×5×12=30$ cm². Two bases: $2×30=60$ cm².

Step3: Calculate lateral area

Perimeter of base: $5+12+13=30$ cm. Lateral area: $30×4=120$ cm².

Step4: Total surface area

Sum: $60+120=180$ cm²? Wait correction: Wait the length is 4cm? Wait no, wait the prism's length (distance between triangular bases) is 4cm? Wait no, wait the triangular sides are 5,12,13 (base triangle) and the prism height (length) is 4cm. Wait no, wait surface area of triangular prism is 2×base area + perimeter×length. So 2×30 + (5+12+13)×4 =60 +30×4=60+120=180? But wait the options have 180 cm² as an option. Oh yes, so the answer is 180 cm².

Wait correction: Yes, the calculation is correct: 2(1/2512) + (5+12+13)4 =60 + 30*4=60+120=180 cm². So the answer is 180 cm².

Step1: Confirm base triangle

Base is right triangle: $5^2+12^2=13^2$.

Step2: Compute base area

$\frac{1}{2}×5×12=30$ cm². Two bases: $2×30=60$ cm².

Step3: Compute lateral area

Perimeter: $5+12+13=30$ cm. Lateral area: $30×4=120$ cm².

Step4: Total surface area

$60+120=180$ cm².

Answer:

336 cm²