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1. Quadrilateral area calculation formula.
2. Types of exercises on quadrilateral area calculation.
3. Exercises.
1. Quadrilateral area calculation formula
Formula for calculating the area of specific quadrilateral shapes (Denoted as S)
* Calculate the area of a general quadrilateral:
Where: a, b, c, d represent the lengths of the sides
* Calculate the area of a parallelogram:
Where:
- a is the base
- h is the height
* Calculate the area of a square (calculate the area of a square)
Where: a is the side length of the square
* Calculate the area of a rectangle:
Where:
- a represents the length
- b represents the width
* Calculate the area of a rhombus:
Where: d1, d2 respectively are the two diagonals of the rhombus
* Calculate the area of a trapezoid:
Where:
- a, b are the respective base sides of the trapezoid
- h is the perpendicular height from the vertex to the base of the trapezoid
Note: In theory, we can use the area calculation formulas above for all quadrilaterals in plane geometry or in coordinate geometry Oxyz. However, this calculation method may pose certain difficulties for learners. Therefore, in coordinate geometry Oxyz, the area of a quadrilateral is calculated by applying the directed product of two vectors. You will learn this knowledge in the high school mathematics curriculum, so Mytour will not introduce it in this article.
2. Various types of quadrilateral area calculation exercises
In which:
Proof for the above formula:
- S = [(ab + cd)sin B]/2, where B is the angle formed by the two diagonals of the quadrilateral
- S = 2R2sinAsinBsin0, where R is the radius of the circumscribed circle
For Case 2: If the quadrilateral is not cyclic, apply the Bretschneide formula:
* Type 3 : Find the area of any quadrilateral given its 4 sides and two diagonals m, n:
Using the formula: S = [(ab + cd)sin B]/2, where B is the angle formed by the two diagonals of the quadrilateral
3. Exercise: Calculate the area of a quadrilateral
Exercise 1: Calculate the area of a quadrilateral given its 4 sides
Given quadrilateral ABCD, with side AB = 3cm, side BC = 5cm, side CD = 2cm, side DA = 6cm. Given angle A = 110 degrees, angle C = 80 degrees. Find the area of quadrilateral ABCD.
Solution:
According to the formula for finding the area of a quadrilateral, S = 0.5 a.d.sinA + 0.5.b.c.sinC
=> The area of quadrilateral ABCD is S = 0.5*3*6*sin110 + 0.5*5*2*sin 80 = 9*0.939 + 5*0.984 = 8.451 + 4.92 = 13.371 cm2
Therefore, the area of quadrilateral ABCD is 13.371cm2
Exercise 2: Given trapezoid ABCD, with the base sides AB and DC equal to 3 and 7cm respectively, the perpendicular drawn from A to DC intersects at H, AH = 5cm. Calculate the area of trapezoid ABCD.
Solution:
According to the formula for calculating the area of a trapezoid S = (a+b)/2 x h
=> The area of the trapezoid is S = (3 + 7)/2 x 5 = 25 cm2
Therefore, the area of the trapezoid is 25cm2.
Exercise 3: Given quadrilateral ABCD circumscribed, with side lengths AB = 3cm, BC = 5cm, CD = 2cm, DA = 6cm. Calculate the area of quadrilateral ABCD.
Solution:
Thus, with the given article, we have reinforced the methods for calculating the area of a rectangle, a special quadrilateral with four right angles, or the area of any quadrilateral. Refer to these for easier problem-solving.
You can explore more mathematical formulas shared on Mytour to strengthen your understanding of Mathematics, apply them, and solve related exercises. A square is a quite special quadrilateral with parallel and equal sides. Mastering the formula for the perimeter of a square will help you easily solve problems involving the area of a parallelogram.
To remember how to calculate the area of a trapezoid, you can refer to some short and interesting poems that make learning geometric formulas simpler and more enjoyable.
