Respuesta :
to do this you just have to figure out the side lengths. since it is called figure ABCD this means A connects to B and B connects to C and C connects to Dand D connects to A. lets find A
since the y values of A and B are the same, the length is the difference in x values. the difference is -4 - 2 = -6. distance is absolute value of difference so 6.
B and C hace same x values so length is difference in y values. 1 -(-5) = 6
notice for CD the x and y values both change. this means we must use pythagorem theorem. but this also means it is not a square so we cannot do area = length * width to find area. we will havebto make the figure into 2 figures to find area. well will find the area of the square plus the area of the triangle. we will create point E at (2, -3). that creates rectangle ABED. ehich has sides AB = ED and BE = DA. DA has length of the differnece in y values since X values are equal. si 1 -(-3) = 4.
the area of this rectangle is 4 * 6 = 24
we will take triangle of DEC. notice it is a right triangle. if you turn it on its side we have base EC and height of ED. area = 1/2 * base * height. so we know ED = 6 and EC isnthe difference of and E y values, which is 2. so:
area = 1/2 * 2 * 6
area = 6
add triangle and rectangle areas.
total = 6 + 24
total = 30
since the y values of A and B are the same, the length is the difference in x values. the difference is -4 - 2 = -6. distance is absolute value of difference so 6.
B and C hace same x values so length is difference in y values. 1 -(-5) = 6
notice for CD the x and y values both change. this means we must use pythagorem theorem. but this also means it is not a square so we cannot do area = length * width to find area. we will havebto make the figure into 2 figures to find area. well will find the area of the square plus the area of the triangle. we will create point E at (2, -3). that creates rectangle ABED. ehich has sides AB = ED and BE = DA. DA has length of the differnece in y values since X values are equal. si 1 -(-3) = 4.
the area of this rectangle is 4 * 6 = 24
we will take triangle of DEC. notice it is a right triangle. if you turn it on its side we have base EC and height of ED. area = 1/2 * base * height. so we know ED = 6 and EC isnthe difference of and E y values, which is 2. so:
area = 1/2 * 2 * 6
area = 6
add triangle and rectangle areas.
total = 6 + 24
total = 30
The area of the given figure ABCD with respective coordinates is gotten as; A: 24 square units
What is the area of the quadrilateral?
We are given the coordinates of the quadrilateral as; A(−4, 1), B(2, 1), C(2, −5), and D(−4, −3).
By inspection, we see that the y coordinates of A and B are the same. Thus, their length will be the difference of their x coordinates. Thus;
AB = 2 - (-4)
AB = 6
Similarly, B and C have same x coordinates. Thus;
BC = -5 - 1 = -6
A and D have same x coordinate and as such;
AD = -3 - 1 = -4
AB and BC are perpendicular to each other because of opposite signs of same Number and since AD has a different length, then we can say that the figure ABCD is a rectangle.
Thus;
Area of figure = 6 * 4 = 24 square units.
Read more about quadrilateral area at; https://brainly.com/question/5715879
