Question

Find the area of the prism help ASAP!!

Answer 1

To find the surface area of a prism, we must find the area of each side and add them up.

Let's first find the area of the triangular base.

The area of a triangle is $\dfrac{1}{2} bh$
Where b is the base length and h is the height.

The base length of the triangle is 10.5. The height is 10.

$A_B= \dfrac{1}{2}bh= \dfrac{1}{2} \times 10 \times 10.5=52.5$

The triangular base has an area of 52.5 cm².

The triangular top must also have the same area. Thus, it also has an area of 52.5 cm².

Now we to find the length of the 3 rectangles on the side of the prism.

The formula for the area of a rectangle is $A=wl$
where $w$ is the width and $l$ is the length.

All rectangles have a width of 8. They all have different lengths. If we find the area of all the rectangles, we have the following:

$A_1=8 \times 10.5 = 84$

$A_2=8 \times 10 = 80$

$A_3=8 \times 14.5=116$

Now, add up ALL the areas we found. We'll have our surface area once we do this.

$52.5+52.5+84+80+116=385$

The surface area is 385 cm². Hope this helps! :)