Find The Area of A Quadrilateral

  • Thread starter LLS
  • Start date
  • Tags
    Area
My answer is wrong. The correct answer is 2.25. Thank you for the help.In summary, the area of the quadrilateral PQTS is 2.25. This is obtained by finding the area of triangle PQT, which is one-quarter of the area of the square PQRS, and then adding it to the upper half of the square. This results in a total area of three-quarters of the square, or 2.25 units.
  • #1
LLS
40
0
The Area of A Quadrilateral Given A Square

Homework Statement



In a square PQRS, point T is the midpoint of side QR. If the area of square PQRS is 3, what is the area of quadrilateral PQTS?

Homework Equations



area = 1/2 base * height

The Attempt at a Solution



Side QR = 1.737

Side RS = 1.737

TR = .8685

area = 1/2(1.737) * .8685 = .25

The area of the triangle = .25

3 - .25 = 2.75

The area of quadrilateral PQTS = 2.75

Is my answer right?
 
Last edited:
Physics news on Phys.org
  • #2
LLS said:
area = 1/2(1.737) * .8685 = .25

Check your arithmetic here: you have one-half of a number close to 1.8, which you multiplied by a number close to 0.9, and got 0.25...(?)

I have another suggestion. Draw a picture of this square with the line segment PT added. What is the area of triangle PQT? (Incidentally, because of the symmetry of the geometry here, you don't even need to use the formula for the area of a triangle.)

Now, the quadrilateral PQTS is made up of half the square plus a triangle of the same area as PQT. So what would this quadrilateral's area be?
 
Last edited:
  • #3
Sometimes it's easier to stick with whole numbers and fractions:
length of side = [tex]\sqrt{3}[/tex]
length of QT = [tex]\frac{1}{2}[/tex][tex]\sqrt{3}[/tex]

area of triangle QTS = [tex]\frac{1}{2}[/tex]*[tex]\frac{\sqrt{3}}{2}[/tex]*[tex]\sqrt{3}[/tex]
=[tex]\frac{\sqrt{3}}{2}[/tex]*[tex]\frac{\sqrt{3}}{2}[/tex]
and what does [tex]\sqrt{3}[/tex]*[tex]\sqrt{3}[/tex] = ?
divide that by 4 (1/2 * 1/2) for your answer.

Then take that away from 3.
 
  • #4
Dr Zoidburg said:
Sometimes it's easier to stick with whole numbers and fractions:
length of side = [tex]\sqrt{3}[/tex]
length of QT = [tex]\frac{1}{2}[/tex][tex]\sqrt{3}[/tex]

area of triangle QTS = [tex]\frac{1}{2}[/tex]*[tex]\frac{\sqrt{3}}{2}[/tex]*[tex]\sqrt{3}[/tex]
=[tex]\frac{\sqrt{3}}{2}[/tex]*[tex]\frac{\sqrt{3}}{2}[/tex]
and what does [tex]\sqrt{3}[/tex]*[tex]\sqrt{3}[/tex] = ?
divide that by 4 (1/2 * 1/2) for your answer.

Then take that away from 3.

√3*√3 = 3

3 - 3/4 = 2.25

The quad = 2.25?

I don't think that answer is correct.
 
Last edited:
  • #5
I may have mad a mistake in the math. Is the answer 2.75?
 
  • #6
The triangle you are describing has one-quarter the area of the square. (Take the midpoint on the side opposite QR, which is PS. A line straight from T to that other midpoint divides the square in two. The line from P to T divides that rectangle in half diagonally, so triangle PQT has one-quarter of 3 units or 0.75.

The quadrilateral PQTS is made up of the upper half of the square plus a triangle with the same area as PQT. So it has three-quarters of the area of the whole square or
(3/4) · 3 = 2.25 units.
 
  • #7
dynamicsolo said:
The triangle you are describing has one-quarter the area of the square. (Take the midpoint on the side opposite QR, which is PS. A line straight from T to that other midpoint divides the square in two. The line from P to T divides that rectangle in half diagonally, so triangle PQT has one-quarter of 3 units or 0.75.

The quadrilateral PQTS is made up of the upper half of the square plus a triangle with the same area as PQT. So it has three-quarters of the area of the whole square or
(3/4) · 3 = 2.25 units.

Thank you
 

1. What is the formula for finding the area of a quadrilateral?

The formula for finding the area of a quadrilateral depends on the shape of the quadrilateral. For a rectangle or square, the formula is length x width. For a parallelogram, the formula is base x height. For a trapezoid, the formula is (base 1 + base 2) / 2 x height. For a kite or rhombus, the formula is (diagonal 1 x diagonal 2) / 2.

2. How do you find the area of a quadrilateral if only two sides are given?

If only two sides of the quadrilateral are given, you can use the formula for the shape that best fits the given information. For example, if you are given the length and width of a rectangle, you can use the formula length x width to find the area. If you are given the base and height of a parallelogram, you can use the formula base x height to find the area.

3. Can you find the area of a quadrilateral if the angles are unknown?

Yes, you can still find the area of a quadrilateral even if the angles are unknown. You will need to use the formula for the shape that best fits the given information. For example, if you are given the length of all four sides of a kite, you can use the formula (diagonal 1 x diagonal 2) / 2 to find the area.

4. How do you find the area of an irregular quadrilateral?

An irregular quadrilateral is a quadrilateral with no equal sides or angles. To find the area of an irregular quadrilateral, you can divide it into smaller, known shapes (such as triangles or rectangles) and find the area of each shape using the appropriate formula. Then, add the areas of each shape together to find the total area of the quadrilateral.

5. What is the unit of measurement for the area of a quadrilateral?

The unit of measurement for the area of a quadrilateral is always squared. For example, if the sides of the quadrilateral are measured in centimeters, the area will be measured in square centimeters (cm²). If the sides are measured in feet, the area will be measured in square feet (ft²).

Similar threads

  • Precalculus Mathematics Homework Help
Replies
2
Views
978
  • Math POTW for Secondary and High School Students
Replies
2
Views
922
  • Precalculus Mathematics Homework Help
Replies
27
Views
1K
  • Precalculus Mathematics Homework Help
Replies
6
Views
2K
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
3
Views
804
  • Precalculus Mathematics Homework Help
Replies
1
Views
2K
  • Precalculus Mathematics Homework Help
Replies
7
Views
3K
  • Precalculus Mathematics Homework Help
Replies
8
Views
540
  • Precalculus Mathematics Homework Help
Replies
9
Views
1K
Back
Top