The total surface area of a regular quadrangular prism is 102 dm² and the lateral surface area

| July 22, 2021 | education

The total surface area of a regular quadrangular prism is 102 dm² and the lateral surface area is 84 dm². Find the height of the prism.

The total surface area of ​​the prism is equal to the sum of the lateral surface area and the area of ​​the two bases. Find the area of ​​the base:

Sb = (Sp – Sbok): 2 = (102 – 84): 2 = 18: 2 = 9 dm².

The base of a regular prism is a square with an area of ​​9 dm². This means that the side of the base of the prism will be 3 dm (3 * 3 = 9).

The side surface consists of four equal faces. Let’s find the area of ​​one face:

Sgr = Sside: 4 = 84: 4 = 21 dm².

The face of a straight prism is a rectangle with sides equal to the side of the base and the height.

3 * h = 21.

Hence h = 7 dm.

Answer: The height of the prism is 7 dm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.