Question

what is the surface area of the three - dimensional figure? sa = in² area of rectangle a = l·w area of triangle a = $\frac{1}{2}(b·h)$ sa = 2($\frac{1}{2}$)(3·4) + 2(5·5) + 3·5

Explanation:

Step1: Calculate area of triangles

We have 2 triangles with base $b = 3$ and height $h=4$. Using the formula $A=\frac{1}{2}(b\cdot h)$, for 2 triangles, the area is $2\times\frac{1}{2}(3\times4)=3\times4 = 12$.

Step2: Calculate area of two equal - sized rectangles

We have 2 rectangles with length $l = 5$ and width $w = 5$. Using the formula $A=l\cdot w$, the area of these two rectangles is $2(5\times5)=2\times25 = 50$.

Step3: Calculate area of the third rectangle

We have a rectangle with length $l = 5$ and width $w = 3$. Using the formula $A=l\cdot w$, the area is $3\times5=15$.

Step4: Calculate the total surface - area

Add up the areas of all the shapes. $SA=12 + 50+15=77$.

Answer:

77