Answer:
96 cm²
Step-by-step explanation:
Add up the areas of the 2 triangular bases and the 3 rectangular faces.
Each triangular base is a 3-4-5 right triangle, so has an area of ...
A = (1/2)(3 cm)(4 cm) = 6 cm²
The rectangular faces are all 7 cm long. Their widths are 3 cm, 4 cm, and 5 cm, so total (3+4+5) cm = 12 cm. Then the sum of areas of the three rectangular faces is ...
A = (12 cm)(7 cm) = 84 cm²
Adding that to the two triangular faces, we get a total area of ...
total area = rectangular face area + 2·(triangular face area)
= (84 cm²) + 2(6 cm²) = 96 cm²
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About the 3-4-5 triangle
The missing side length of the right triangle can be found using the Pythagorean theorem:
missing side = √(5² -3²) = √16 = 4 . . . . cm
These are the dimensions of the famous 3-4-5 right triangle, one you probably recognize from many problems with the Pythagorean theorem.
The sequential integers 3, 4, 5 are the only set of sequential integers that form a right triangle, and they are the smallest set of integers of any relationship that form a right triangle. It is worth remembering these facts, as you will see these numbers (or this ratio of numbers) often in triangle problems.
