Question

Find the area of the unfolded envelope as shown in the figure given below. (Measures are given in inches.)

• A. $72$ inch${}^2$
• B. $70$ inch${}^2$
• C. $44$ inch${}^2$

Answer 1

The correct option is A $72$ inch${}^2$


Area of the unfolded envelope = Area of Triangle above the rectangle + Area of the triangle to the left of rectangle + Area of triangle to the right of rectangle + Area of Triangle below the rectangle + Area of rectangle

Area of the triangle above the rectangle $=\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times 7\times 4$
$=14$ inch${}^2$

Area of triangle to the left of rectangle
$=\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times 4\times 4$
$=8$ inch${}^2$

Area of triangle to the right of rectangle $=\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times 4\times 4$
$=8$ inch${}^2$

Area of triangle below the rectangle $=\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times 7\times 4$
$=14$ inch${}^2$

Area of rectangle $=length\times width$
$=7\times 4$
$=28$ inch${}^2$

Area of the unfolded envelope$=14+8+8+14+28$
$=72$ inch${}^2$