find the lateral surface area of the prism. lsa = ? cm²

Explanation:

Step1: Identify lateral - face dimensions

The lateral faces of the prism are three rectangles. Two have dimensions 7 cm by 3 cm and 7 cm by 4 cm, and one has dimensions 7 cm by 5 cm.

Step2: Calculate area of first rectangle

The area of a rectangle is $A = l\times w$. For the rectangle with $l = 7$ cm and $w = 3$ cm, $A_1=7\times3 = 21$ $cm^2$.

Step3: Calculate area of second rectangle

For the rectangle with $l = 7$ cm and $w = 4$ cm, $A_2=7\times4 = 28$ $cm^2$.

Step4: Calculate area of third rectangle

For the rectangle with $l = 7$ cm and $w = 5$ cm, $A_3=7\times5 = 35$ $cm^2$.

Step5: Calculate lateral - surface area

The lateral - surface area (LSA) is the sum of the areas of the lateral faces. $LSA=A_1 + A_2+A_3$. $LSA=21 + 28+35$. $LSA = 84$ $cm^2$.

Answer:

84