What is the total area of this prism?
t. a=

The answer to your question is 61.8 in²

Step-by-step explanation:

Process

1.- Calculate the height of the triangle

    3² = h² + 1.5²

    h² = 3² - 1.5²

    h² = 9 - 2.25

    h² = 6.75

    h = 2.6 in

2.- Calculate the area of the triangles

     Area =

     Area =

     Area = 3.9 in²

    There are 2 triangles = 2(3.9) = 7.8 in²

3.- Calculate the area of the rectangles

     Area = base x height

     Area = 6 x 3 = 18 in²

     There are 3 rectangles = 3(18) = 54 in²

4.- Total area

     At = 7.8 + 54

         = 61.8 in²

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584