PLZZZZZ HELP I SUCK AT GEOMETRY
Find the area of the following shape. You must show all work to receive credit.
Figure ABCDEF is shown. A is located at negative 2, 6. B is located at negative 5, 2. C is located at negative 2, negative 3. D is located at 4, negative 3. E is located at 5, 3. F is located at 1, 3.
Divide it up into rectangles and triangles, which are easy to figure.
How would I divided it up into a rectangle and triangle can you please show me how?
To find the area of the given shape, we can divide it into smaller shapes and then find the area of each shape separately.
Step 1: Calculate the length of AB:
Using the distance formula:
Length AB = √(x₂ - x₁)² + (y₂ - y₁)²
Substituting the coordinates of A and B:
Length AB = √((-5 - (-2))² + (2 - 6)²)
= √(-3² + (-4)²)
= √(9 + 16)
= √25
= 5
Step 2: Calculate the length of BC:
Using the distance formula:
Length BC = √(x₂ - x₁)² + (y₂ - y₁)²
Substituting the coordinates of B and C:
Length BC = √((-2 - (-5))² + (-3 - 2)²)
= √(3² + (-5)²)
= √(9 + 25)
= √34
Step 3: Calculate the length of CD:
Using the distance formula:
Length CD = √(x₂ - x₁)² + (y₂ - y₁)²
Substituting the coordinates of C and D:
Length CD = √((4 - (-2))² + (-3 - (-3))²)
= √(6² + 0²)
= √36
= 6
Step 4: Calculate the area of triangle ABC:
Using the formula for the area of a triangle:
Area of triangle ABC = ½ * base * height
Substituting the values for base (AB = 5) and height (BC = √34):
Area of triangle ABC = ½ * 5 * √34
Step 5: Calculate the area of rectangle CDEF:
Length of the rectangle = CD = 6
Width of the rectangle = Length of DE = √((5 - 4)² + (3 - (-3))²) = √(1² + 6²) = √37
Area of rectangle CDEF = Length * Width = 6 * √37
Step 6: Calculate the total area of the given shape:
Total area = Area of triangle ABC + Area of rectangle CDEF
Total area = ½ * 5 * √34 + 6 * √37
Thus, the total area of the given shape is ½ * 5 * √34 + 6 * √37 (units squared).
To find the area of the shape ABCDEF, we can divide it into two triangles and a rectangle:
1. Triangle ABC: This triangle is formed by connecting points A, B, and C. To find its area, we can use the formula for the area of a triangle:
Area_ABC = 0.5 * base * height
The base of triangle ABC is the horizontal distance between points A and B, which is |x_A - x_B| = |-2 - (-5)| = 3.
The height of triangle ABC is the vertical distance between point A and the line segment BC, which is |y_A - y_C| = |6 - (-3)| = 9.
Plugging in these values into the formula, we get:
Area_ABC = 0.5 * 3 * 9 = 13.5
2. Rectangle BCDE: This rectangle is formed by connecting points B, C, D, and E. To find its area, we can use the formula for the area of a rectangle:
Area_BCDE = length * width
The length of rectangle BCDE is the horizontal distance between points B and E, which is |x_B - x_E| = |-5 - 5| = 10.
The width of rectangle BCDE is the vertical distance between points B and C, which is |y_B - y_C| = |2 - (-3)| = 5.
Plugging in these values into the formula, we get:
Area_BCDE = 10 * 5 = 50
3. Triangle CDEF: This triangle is formed by connecting points C, D, and E. To find its area, we can use the formula for the area of a triangle:
Area_CDEF = 0.5 * base * height
The base of triangle CDEF is the horizontal distance between points C and D, which is |x_C - x_D| = |-2 - 4| = 6.
The height of triangle CDEF is the vertical distance between point C and point E, which is |y_C - y_E| = |-3 - 3| = 6.
Plugging in these values into the formula, we get:
Area_CDEF = 0.5 * 6 * 6 = 18
To find the total area of the shape ABCDEF, we add the areas of the two triangles and the rectangle:
Total Area = Area_ABC + Area_BCDE + Area_CDEF
= 13.5 + 50 + 18
= 81.5 square units
Therefore, the area of the given shape is 81.5 square units.