Answer:
Explanation:
Remark
There are many ways you can do this. I think the simplest way is to find the area of the rectangle enclosing the winged shape and take away the area of the three unshaded triangles.
Area of enclosed rectangle
Area = L * w
L = 26 in
w = 15 in
Area = 26 * 15
Area = 390 square inches.
Find the area of the triangle on the right.
Area = 1/2 * b * h
base = 26 inches
height = 15 - 6 = 9
This is a little tricky. What you need to do to get the height of the triangle is realize that it is made from a line that goes from the base of the triangle to its peak. This line is perpendicular to the base. The line you just drew is 15 inches tall, same as the width of the enclosing rectangle.
Substitute values into the formula
Area = 1/2 * 26 * 9
Area = 117 square inches.
Find the area of the top and bottom triangles.
These 2 triangles are the same sort of thing only the base requres a bit of manipulation
height = 15 inches
base = (26 - 14)/2
base = 12/2
base = 6
Again, this requires a little bit of thought. You have 2 bases making up each of the right triangles. To find the sum of both of them, you take 26 and subtract 14 from it. That's where the 12 comes from. Now you divide 2 to get the base of each of the triangles. That gives you 6.
Find the area of one of the triangles.
Area = 1/2 * b * h
Area = 1/2 * 6 * 15
Area = 45 square inches
Find the area of both triangles.
Area of triangles at the top and bottom = 2*45 = 90
Finally find the area of the shaded area.
Area = enclosed rectangle - top triangle and bottom triangle - the triangle on the right.
Area shaded area = 390 - 45 - 45 - 117 = 183
Answer: Area shaded region = 183 square inches.