Question

23 the net of a triangular prism is shown with dimensions in centimeters. 20 cm 13 cm l×b 10 cm 12 cm 13 cm ½ bh 20×13=260 what is the total surface area of the triangular prism in square centimeters? a 900 cm² b 850 cm² c 720 cm² d 840 cm²

Explanation:

Step1: Calculate area of triangular faces

The formula for the area of a triangle is $\frac{1}{2} \times base \times height$. Here, base = 10 cm, height = 12 cm. So area of one triangle is $\frac{1}{2} \times 10 \times 12 = 60$ $cm^2$. There are 2 triangular faces, so total area for triangles is $2 \times 60 = 120$ $cm^2$.

Step2: Calculate area of rectangular faces

First rectangle: dimensions 20 cm (length) and 13 cm (width). Area = $20 \times 13 = 260$ $cm^2$. There are two such rectangles (top and bottom), so area for these two is $2 \times 260 = 520$ $cm^2$.

Second rectangle: dimensions 20 cm (length) and 10 cm (width). Area = $20 \times 10 = 200$ $cm^2$. There is one such rectangle (middle).

Step3: Sum all areas

Total surface area = area of triangles + area of two 20x13 rectangles + area of 20x10 rectangle. So $120 + 520 + 200 = 840$ $cm^2$.

Answer:

D. $840\ cm^2$ (assuming option D is the one with 840, as per the marked check in the image)