Question

a net for a three - dimensional figure is shown on grid paper. each square of the grid paper represents 1 in². what is the surface area of the three - dimensional figure? s.a. = in² area of rectangle a = l·w area of triangle a = 1/2(b·h) s.a. = 2(1/2(3·4))+2(5·5)+3·5

Explanation:

Step1: Calculate area of triangles

The formula for the area of a triangle is $A=\frac{1}{2}(b\cdot h)$. Here, for the two congruent triangles, $b = 3$ and $h=4$. The combined area of the two triangles is $2\times\frac{1}{2}(3\times4)=3\times4 = 12$.

Step2: Calculate area of larger rectangles

There are two larger rectangles with length $l = 5$ and width $w = 5$. The combined area of these two rectangles is $2\times(5\times5)=50$.

Step3: Calculate area of smaller rectangle

The smaller rectangle has length $l = 3$ and width $w = 5$. Its area is $3\times5=15$.

Step4: Calculate total surface - area

The surface - area formula given is $S.A.=2\times\frac{1}{2}(3\times4)+2\times(5\times5)+3\times5$. Add the areas from the previous steps: $12 + 50+15=77$.

Answer:

77