Table of Contents
- 1 What is the biggest possible area of a quadrilateral with sides of length 1 4 7 and 8?
- 2 Which type of quadrilateral will maximize the area of a quadrilateral?
- 3 What is the maximum possible area of a quadrilateral with a perimeter of 80 cm?
- 4 What is a concyclic quadrilateral?
- 5 How do you find the area of a rectangle with sides?
What is the biggest possible area of a quadrilateral with sides of length 1 4 7 and 8?
So the area of the quadrilateral is sum of the areas of both the triangles. = 28 square units.
Which type of quadrilateral will maximize the area of a quadrilateral?
The quadrilateral with given side lengths that has the maximum area is the cyclic quadrilateral.
What is the maximum possible area of a quadrilateral with a perimeter of 80 cm?
In this question the perimeter is 80 units. To find the sides of our rectangle divide 80 units by 4 to get 20 units. The area of the rectangle is length*width which in this question is 20 units *20 units = 400 square units. The maximum area is 400 square units.
How do you maximize one area of a quadrilateral?
In case of quadrilateral, two triangles are formed on each side of diagonal. In the first option, hypotenuse of 7 and 8 will large to permit 1 and 4 to form a triangle. In the second option, 7 and 4 make hypotenuse value as 8.1, which is less than sum of 8+1=9. This is a valid option to maximize one of the triangles areas.
What is the maximum area of a quadrilateral with hypotenuse 8?
Area is ½ ab SinC. Means maximum area is when C=90 deg. In case of quadrilateral, two triangles are formed on each side of diagonal. In the first option, hypotenuse of 7 and 8 will large to permit 1 and 4 to form a triangle. In the second option, 7 and 4 make hypotenuse value as 8.1, which is less than sum of 8+1=9.
What is a concyclic quadrilateral?
A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. The circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. In the above image above r is the radius of the circumcircle and A, B, C, and D are the lengths of the sides PQ, QR, RS, and SP respectively.
How do you find the area of a rectangle with sides?
If you have a rectangle (figure A), with sides X and Y and Area = X x Y, and you do not change the length of the sides but change the angle formed by sides X and Y (i.e. decrease from 90 to 85 degrees)to make figure B, why is the area of figure B (calculated by the formula 1/2 B x H) now less than figure A?