116k views
1 vote
The base of a three-sided prism is an isosceles triangle with a base of length 80 cm and a side of length 41 cm. Calculate the area of ​​the prism if the length of the height of the prism is equal to the length of the height of the lenght of base.

Is my anwer correct? ​

The base of a three-sided prism is an isosceles triangle with a base of length 80 cm-example-1

1 Answer

5 votes

Explanation:

I think the problem definition degraded a bit, when you transferred it over to here.

so, let me try to rephrase this properly, and I hope that my interpretation fits the original problem.

the base of a 3-sided prism is an isoceles triangle with a baseline length of 80 cm, and a side length of 41 cm.

calculate the surface area of the prism, if the length of the height of the prism is equal to the height of the base triangle to its baseline.

let's go through this step by step (even the ones you skipped) :

first : isoceles means that both legs are equally long. so, the prism base is a 80 - 41 - 41 triangle.

the height to its baseline is therefore splitting the baseline in the middle (into 2 equal parts) : 2×40 cm.

therefore it is also splitting the whole main triangle into 2 equal right-angled triangles (half of the baseline, a leg of the main triangle, and the height of the main triangle to the baseline).

now that we have right-angled triangles, we can use Pythagoras to calculate the height, as the leg of the main triangle is now the baseline of the "half" right-angled triangle :

41² = 40² + height²

1681 = 1600 + height²

81 = height²

height = 9 cm

so, the height to the baseline of the main triangle is 9 cm, and so is per definition the height of the prism.

that means, no, you were not correct. I honestly don't know what you did there at the beginning with the height calculation.

but let's continue.

so, the base and the top of the prism are such equal isoceles triangles.

the sides of the prism are (3) rectangles :

one is 80×9 cm²

and the other two are 41×9 cm² each

the area of a triangle is

baseline × height / 2

in our case

80 × 9 / 2 = 40 × 9 = 360 cm²

we have 2 such triangles (base and top) :

2 × 360 = 720 cm²

the areas of the rectangles are

80 × 9 = 720 cm²

41 × 9 × 2 = 738 cm²

so, the total surface area of the prism is

720 + 720 + 738 = 2178 cm²

FYI

if you were looking for the volume of the prism, that would be

base area × prism height = 360 × 9 = 3240 cm³

No related questions found