Answer:
392 square inches
Explanation:
To solve this we need to look at this quadrilateral as two shapes that share a side - a triangle and a rectangle.
You can see in the attatchment how I have drawn a dotted line indicating where they share a side.
From here we find the area of each shape seperately and add those areas together!
Rectangle:
Looking at the rectangle portion we can see that the width is 16 in and the length is 19 inches. Don't be fooled by the long 30 inch side. Remember, we are only looking at the portion that makes up the rectangle.
A = l*w = 16*19 = 304 inches squared
Triangle:
To find the area of the triangle, we use the formula A = (b*h)/2 where b = the length of the base and h = the height.
We can see in this attatched drawing that the height of the triangle is the same length as the width of the rectangle which is 16 inches.
To find the base, you can do one of two things.
1) use the pythagorian theorem (A^2 + B^2 = C^2) to solve for the missing side of the right triangle, where A is 16 inches, B is unknown and C is 19.4 inches.
2) *easier* using the information given, we can see that the longest side of this shape is 30 inches and is made up of the length of the rectangle (19 inches) and the base of the triangle (which is unkown - we can call it x)
Given that we know the total length and the length of the portion that belongs to the rectangle, we can say x = 30-19 = 11. Therefore the base of the rectangle is 11 inches.
From here we use b*h/2
11*16/2 = 88 = area of the triangle in square inches.
Now for the easy part - add up the areas for the total!
Area (rectangle) + Area (triangle) = Area (total)
304 + 88 = 392 square inches