Answer:
Perimeter = 27 ft
Area = 34.2 ft²
Height = 13 ft
Step-by-step explanation:
Perimeter of the Triangular Base
The perimeter of the triangular base is the sum of the lengths of its three sides. Therefore:
[tex]\sf Perimeter = 10+8+9\\\\Perimeter = 27\;ft[/tex]
So, the perimeter of the triangular base is:
[tex]\Large\boxed{\boxed{\sf Perimeter = 27 \;feet}}[/tex]
[tex]\dotfill[/tex]
Area of the Triangular base
To find the area of the triangular base, we can use the formula for the area of a triangle, which is half the product of its base and height.
In this case, the base of the triangle is 9 ft, and its height is 7.6 ft. Therefore:
[tex]\sf Area=\dfrac{1}{2} (9 \cdot 7.6)\\\\\\Area=\dfrac{1}{2}(68.4)\\\\\\Area=34.2\; ft^2[/tex]
So, the area of the triangular base is:
[tex]\Large\boxed{\boxed{\sf Area =34.2\; square\; feet}}[/tex]
[tex]\dotfill[/tex]
Height of the Prism
The bases of a prism are the two parallel polygonal faces that determine its shape. These bases are congruent and situated opposite each other. The height of a prism is the perpendicular distance between these parallel bases.
In this case, the parallel bases are triangles. So, the height of the prism is the perpendicular distance between the two triangular bases. Therefore, the height of the prism is:
[tex]\Large\boxed{\boxed{\sf Height= 13 \;feet}}[/tex]
