Given:
The figure and dimensions of the triangular prism.
The base is an isosceles triangle
To find:
The area of the triangular prism.
Solution:
The area of a triangle is:
[tex]A_1=\dfrac{1}{2}\times base\times height[/tex]
The base of the triangle is 24 cm and the height is 35 cm. So, the area of a triangular base (in sq. cm) is:
[tex]A_1=\dfrac{1}{2}\times 24\times 35[/tex]
[tex]A_1=12\times 35[/tex]
[tex]A_1=420[/tex]
The bases of the triangular prism are same. So, the area of the other triangular base is [tex]A_2=420[/tex] sq. cm.
The sides of the base triangle are 37 cm, 37 cm and 24 cm. So, the perimeter of the base triangle is:
[tex]P=37+37+24[/tex]
[tex]P=98[/tex]
Now, the curved surface area of the prism is:
[tex]A_3=P\times h[/tex]
Where, P is the base perimeter and h is the height of the prism.
The base perimeter of the triangular prism is 98 cm and the height is 48 cm. So, the curved surface area is:
[tex]A_3=98\times 48[/tex]
[tex]A_3=4704[/tex]
Now, the total area of the triangular prism is:
[tex]A=A_1+A_2+A_3[/tex]
[tex]A=420+420+4704[/tex]
[tex]A=5544[/tex]
Therefore, the area of the given triangular prism is 5544 sq. cm.
