Question

What is the area of parallelogram ABCD in square units

Answer 1

My way of solving this if to make four triangles and one rectangle out of this shape.


Use AB, BC, CD, DA to make the triangles.
The left-overs make up a rectangle that has the area of 2x3, which is 6.

Triangle AB and CD are equivalent, they are both (1/2)(1)(3)=1.5 each, which add up to 3.

Triangle AD and BC are equivalent, they are both (1/2)(1)(4)=2 each, which add up to 4.

So, just add up the 6 from the rectangle and the 3 & 4 and you get 13.

The area of that parallelogram is 13.

Answer 2

13 square units

Further explanation

Consider attachment for details.

We make a KLMN rectangle that touches all the vertices of the ABCD parallelogram. Consequently, the ABCD parallelogram is right inside the KLMN rectangle.

Let us take the following strategic steps:

• Calculate the area of KLMN.
• Calculate the area of the triangles ABL, CDM, ADK, and BCN.
• Subtract the area of the KLMN rectangle with the area of all triangles.
• The difference in the area above is the area of the ABCD parallelogram.

The Process:

• The area of KLMN = 4 x 5 = $\boxed{ \ 20 \ square \ units. \ }$
• The ADK triangle is congruent to the BCN triangle, and each area is $\boxed{ \ \frac{1}{2} \times 4 \times 1 = 2 \ square \ units. \ }$ Thus the total area of ADK and BCN is $\boxed{ \ 2 + 2 = 4 \ square \ units. \ }$
• The ABL triangle is congruent to the CDM triangle, and each area is $\boxed{ \ \frac{1}{2} \times 3 \times 1 = 1.5 \ square \ units \ }.$ Thus, the combined area of ABL and CDM is $\boxed{ \ 1.5 + 1.5 = 3 \ square \ units. \ }$
• Finally, the area of ABCD = 20 - 4 - 3 = 13.

As a result, we get the area of the parallelogram ABCD is 13 square units.

Learn more

1. A triangle is rotated 90° about the origin brainly.com/question/2992432
2. Find out the coordinates of the image of a vertex after the triangle is rotated 270° about the origin brainly.com/question/7437053
3. The midpoint brainly.com/question/3269852

Keywords: what is the area of parallelogram ABCD, in square units, graph, cartesian coordinates, triangle, rectangular, congruent, touches all the vertices