Answer:
108 m^2
Explanation:
To find the area of this shape, we will separate it into two shapes. A rectangle and a triangle. Draw a line at the right end of the 15 m arrow, so we get a rectangle and a triangle.
Now we have two separate shapes that we will find the area of separately and add the area of both shapes to find the area of the shape in the image.
Rectangle
So first we have a rectangle.
The formula for the area of a rectangle is:
A = l * w
Where A is the area, l is the length, and w is the width.
For this rectangle, we have 15 m for length, and 6 m for width.
So we will put it in the formula and get:
A = 15 m * 6 m
A = 90 m^2
Remember area is squared.
Triangle
Now that we solved the area for the rectangle, we will solve the area of the triangle.
The formula for the area of a triangle is:
A = 1/2 (b * h)
Where A is the area, b is the base, and h is the height.
We know that the base of the triangle is 6 m, same as the width of the rectangle. But for the height, we must do a simple calculation.
The total length of this shape is 21 m, and the length of the rectangle is 15 m, so the rest of the length is the height of the triangle. We will subtract the total length of the shape by the length of the rectangle to find the height of the triangle.
21 m - 15 m = 6 m
So the base of the triangle is 6 m and the height is also 6 m.
Putting these numbers in the formula, we get:
A = 1/2 (6 m * 6 m)
Multiply the numbers in the parentheses first, following PEMDAS:
A = 1/2 (36 m^2)
A = 18 m^2
So now we have the areas of both the rectangle and triangle.
Area of rectangle = 90 m^2
Area of triangle = 18 m^2
Now to get our final answer, the area of the shape in the image, we will add the two areas we found.
90 m^2 + 18 m^2 = 108 m^2
The area of the shape below is 108 m^2.