find the surface area of this triangular prism. sa = m²
find the surface area of this triangular prism. sa = m²
Answer
Explanation:
Step1: Calculate the area of the triangular bases
The formula for the area of a triangle is (A=\frac{1}{2}bh). Here, (b = 3m) and (h=4m). (A_{triangle}=\frac{1}{2}\times3\times4=6m^{2}). Since there are 2 triangular bases, (2\times A_{triangle}=2\times6 = 12m^{2})
Step2: Calculate the area of the rectangular faces
There are 3 rectangular faces.
- For the face with sides (3m) and (6m): (A_{1}=3\times6 = 18m^{2})
- For the face with sides (4m) and (6m): (A_{2}=4\times6=24m^{2})
- For the face with sides (5m) and (6m): (A_{3}=5\times6 = 30m^{2})
The sum of the areas of the rectangular faces is (A_{rectangles}=18 + 24+30=72m^{2})
Step3: Calculate the total surface area
The total surface area (SA) of the triangular prism is the sum of the areas of the triangular bases and the rectangular faces. (SA=12 + 72)
Answer:
(84)