Question

a gift box is in the shape of a right triangular prism. the net of the gift box is shown. which of the following expressions represents the total surface area, in square inches, of the gift box? ① (4×4)+(4×5)+(4×6)+\frac{1}{2}(4×4)+\frac{1}{2}(4×4) ② (4×5)+(4×5)+(4×6)+\frac{1}{2}(4×6)+\frac{1}{2}(4×6) ③ (4×4)+(4×5)+(4×6)+\frac{1}{2}(4×5)+\frac{1}{2}(4×5) ④ (4×5)+(4×6)+(4×6)+\frac{1}{2}(4×6)+\frac{1}{2}(4×6)

Explanation:

Step1: Identify the faces of the prism

The right - triangular prism has 2 triangular faces and 3 rectangular faces.

Step2: Analyze the dimensions of rectangular faces

There are two rectangles with dimensions 4 in×5 in and one rectangle with dimensions 4 in×6 in.

Step3: Analyze the dimensions of triangular faces

The two triangular faces are congruent right - triangles with base 4 in and height 6 in. The area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 4$ in and $h = 6$ in.

Step4: Calculate the total surface area

The total surface area of the prism is the sum of the areas of all its faces. The areas of the rectangles are $(4\times5)+(4\times5)+(4\times6)$ and the areas of the two triangles are $\frac{1}{2}(4\times6)+\frac{1}{2}(4\times6)$.

Answer:

B. $(4\times5)+(4\times5)+(4\times6)+\frac{1}{2}(4\times6)+\frac{1}{2}(4\times6)$