What is the area of trapezoid defg with coordinates d (2, 3), e (4, 3), f (6, 1), and g (2, 1)?

12 square units

8 square units

6 square units

3 square units

Step-by-step explanation

Area of a trapezium is given as

A = ½ (a + b)h

From the attachment we can find a by using co-ordinate geometry

The distance between point "d" and "e" is the required distance "a"

So,

Point 1 = d = (x1,y1) = (2,3)

Point 2 = e = (x2,y2) = (4,3)

distance = √(x2-x1)²+(y2-y1)²

a = √(4-2)²+(3-3)²

a = √2²+0² = √4+0 = √4

a = 2

Also, from the attachment to get "b"

Using the same approach

The distance between point "g" and "f" is the required distance "b"

So,

Point 1 = g = (x1,y1) = (2,1)

Point 2 = f = (x2,y2) = (6,1)

distance = √(x2-x1)²+(y2-y1)²

b = √(6-2)²+(1-1)²

b = √4²+0² = √16+0 = √16

b = 4

Also, to get the height h, we use same approach

The distance between point "d" and "g" is the required distance "h"

So,

Point 1 = d = (x1,y1) = (2,3)

Point 2 = g = (x2,y2) = (2,1)

distance = √(x2-x1)²+(y2-y1)²

h = √(2-2)²+(3-1)²

h = √0²+2² = √0+4 = √4

h = 2

Then, we have the parameters for the area of the trapezium

a = 2, b = 4 and h = 2

Then,

Area = ½ (a+b)•h

Area = ½ × (2+4) × 2

Area = ½ × 6 × 2

Area = 6 Square units

The area of the trapezium is 6 Square units