QuestionCalculate the area of quadrilateral $ABCD$ with vertices $A(0,2)$ , $B(4,7)$ , $C(8,2)$ , $D(4,3)$ .

Studdy Solution

STEP 1

Assumptions1. The coordinates of the vertices of the quadrilateral are given as A(0,), B(4,7), C(8,), and D(4,3). . The area of the quadrilateral can be found by dividing it into two triangles and finding the area of each triangle.

STEP 2

First, let's divide the quadrilateral into two triangles, ABC and ACD.

STEP 3

We will use the formula for the area of a triangle given by coordinates of its vertices. The formula is $Area = \frac{1}{2} |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|$

STEP 4

Let's find the area of triangle ABC. Substituting the coordinates of A, B, and C into the formula, we get $Area_{ABC} = \frac{1}{2} |0(7 -2) +4(2 -2) +8*(2 -7)|$

STEP 5

Calculate the area of triangle ABC.
$Area_{ABC} = \frac{1}{2} |0 -0 -40| = \frac{1}{2} *40 =20$

STEP 6

Now, let's find the area of triangle ACD. Substituting the coordinates of A, C, and D into the formula, we get $Area_{AC} = \frac{1}{2} |0(2 -3) +8(3 -2) +4*(2 -2)|$

STEP 7

Calculate the area of triangle ACD.
$Area_{AC} = \frac{1}{2} |0 - +0| = \frac{1}{2} * =4$

STEP 8

Now that we have the areas of both triangles, we can find the area of the quadrilateral ABC by adding the areas of the two triangles.
$Area_{ABCD} = Area_{ABC} + Area_{AC}$

STEP 9

Substitute the values of the areas of the triangles into the formula.
$Area_{ABCD} =20 +4$

STEP 10

Calculate the area of the quadrilateral ABC.
$Area_{ABCD} =20 +4 =24$ The area of the quadrilateral ABC is24 square units.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms