Question

find the surface area of this prism. surface area of a prism la = hp sa = la + 2b sa = ? cm²

Explanation:

Step1: Calculate the perimeter \(P\) of the base

The base is a rectangle with length \(l = 10\) cm and width \(w=3\) cm. The perimeter formula for a rectangle is \(P = 2(l + w)\).

$$ P=2(10 + 3)=2\times13 = 26\space\text{cm} $$

Step2: Calculate the lateral - area \(LA\)

The height \(h\) of the prism (distance between the two bases) is \(h = 5\) cm. Using the formula \(LA=hP\).

$$ LA = 5\times26=130\space\text{cm}^2 $$

Step3: Calculate the area \(B\) of the base

The area formula for a rectangle (base) is \(B=l\times w\).

$$ B=10\times3 = 30\space\text{cm}^2 $$

Step4: Calculate the surface - area \(SA\)

Using the formula \(SA=LA + 2B\).

$$ SA=130+2\times30=130 + 60=190\space\text{cm}^2 $$

Answer:

\(190\)