Question

find the surface area of this triangular prism. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate the area of the triangular bases

The formula for the area of a right - triangle is $A=\frac{1}{2}\times base\times height$. Here, the base is $10m$ and the height is $24m$.

$$A_{triangle}=\frac{1}{2}\times10\times24 = 120m^{2}$$

Since there are two triangular bases, the combined area of the triangular bases is $2\times120 = 240m^{2}$.

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the rectangle with sides $10m$ and $26m$: $A_{1}=10\times26=260m^{2}$
• For the rectangle with sides $24m$ and $26m$: $A_{2}=24\times26 = 624m^{2}$
• For the rectangle with sides $26m$ and $26m$ (hypotenuse of the right - triangle: using the Pythagorean theorem $c=\sqrt{10^{2}+24^{2}}=\sqrt{100 + 576}=\sqrt{676}=26m$): $A_{3}=26\times26=676m^{2}$

The sum of the areas of the rectangular faces is $A_{rectangles}=260 + 624+676=1560m^{2}$

Step3: Calculate the total surface area

The total surface area of the triangular prism is the sum of the areas of the triangular bases and the rectangular faces.

$$A = 240+1560=1800m^{2}$$

Answer:

$1800m^{2}$