Check the picture below.
[tex]\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=8\\ h=10 \end{cases}\implies A=\cfrac{1}{2}(8)(10)\implies A=40[/tex]
The area of a vertical cross-section through the centre of the base of the party hat is 40 square inches.
It is defined as the three-dimensional shape in which the base is a circular shape and if we go from circular base to top the diameter of the circle reduces and at the vertex, it becomes almost zero.
Clyde has a cone-shaped party hat.
The height of the hat = 10 inches
The radius of the base of the hat = 4 inches.
The diameter of the base of the hat = 2×4 ⇒8 inches
The vertical cross-section of the cone exactly looks like a triangle.
In this scenario, the vertical cross-section of the hat is a triangle with a height of 10 inches, and base length of 8 inches.
We know the formula for the area of a triangle is given by:
[tex]\rm A = \frac{1}{2} (b\times h)[/tex]
Here b = 8 inches, and h = 10 inches
[tex]\rm A = \frac{1}{2} (8\times 10)[/tex]
A = 40 square inches
Thus, the area of a vertical cross-section through the centre of the base of the party hat is 40 square inches.
Learn more about the cone here:
brainly.com/question/16394302
