What is the surface area of the right prism given below?

Mathematics

2 answers:

posledela2 years ago

5 0

Answer: Option D.

Step-by-step explanation:

You can calculate the surface area of this right prism by adding the area of its faces.

You can observe that the faces of the right prism are: Three different rectangles and two equal triangles.

The formula for calculate the area of a rectangle is:

$A=lw$

Where "l" is the lenght and "w" is the width.

The formula for calculate the area of a triangle is:

$A=\frac{bh}{2}$

Where "b" is the base and "h" is the height.

You can observe that the hypotenuse of the each triangle is the width of one of the larger rectangle, then , you can find its value with the Pythagorean Theorem:

$a=\sqrt{b^2+c^2}$

Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

Then, this is:

$a=\sqrt{(8units)^2+(15units)^2}=17units$

Therefore, you can add the areas of the faces to find the surface area of the right prism (Since the triangles are equal, you can multiply the area of one of them by 2). This is:

$SA=(10units)(8units)+(15units)(10units)+(17units)(10units)+2(\frac{(15units)(8units)}{2})\\\\SA=520units^2$