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Akimi4 [234]
3 years ago
5

An 8-sided die is formed when two square pyramids are attached by their bases. The perimeter of the base shape is 6 centimeters.

The distance between the tallest points of the two pyramids is 2 centimeters. What is the surface area of the 8-sided figure?
Mathematics
2 answers:
Leona [35]3 years ago
5 0
Consider one pyramid
Side length of base = 1.5cm and its height is 1 cm
Slant height of one of the lateral faces =  sqrt(1^2 + 0.75^2) =  1.25 cm
Area of one of the triangular faces = 0.5 * 1.5* 1.25 =  0.9375 cm^2

There are 8  of these so the required surface area = 8 * 0.9375 
=  7.5 cm^2 Answer

My name is Ann [436]3 years ago
4 0

Answer:

<em>The surface area of the 8-sided figure is 7.5 cm²</em>

Step-by-step explanation:

The perimeter of the base of each square pyramid is 6 centimeters.

So, <u>each side length of the base</u>  =\frac{6}{4}= 1.5\ cm.

Two pyramids are attached by their bases and the distance between the tallest points of the two pyramids is 2 centimeters.

So, <u>the height of each pyramid</u> = 1 centimeter.

Now, <u>lateral surface area of each pyramid</u>

=2a\sqrt{\frac{a^2}{4}+h^2}

=2(1.5)\sqrt{\frac{(1.5)^2}{4}+(1)^2}\\ \\ =3\sqrt{\frac{2.25}{4}+1}\\ \\ =3\sqrt{1.5625}\\ \\ =3(1.25)=3.75\ cm^2

So, the <u>total lateral surface area of two pyramids</u>  =2(3.75)=7.5\ cm^2

Hence, the surface area of the 8-sided figure is 7.5 cm²

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