solution of the questions The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively, and the angle between the first two sides is a right angle. Find its area.
use Heron's formula.
draw a line from the end of the 6 and 8 cm side, forming a right triangle. The length of that is 10 cm (Pythagorean)
Now you have two triangles. Figure the area of each using Heron's formula,then add them.
semiperimert s=1/2 (a+b+c) on each triangle
Area=sqrt[(s-a)(s-b)(s-c)s] HERO's formula
do that for both triangles, then add.
To find the area of a quadrilateral, we can use Heron's formula. However, since we already know that the angle between the first two sides (6 cm and 8 cm) is a right angle, we can treat the quadrilateral as a rectangle.
To find the area of a rectangle, we can use the formula A = length × width.
In this case, the length of the rectangle would be the longer side, which is 14 cm, and the width would be the shorter side, which is 6 cm.
So, the area of the quadrilateral ABCD would be:
A = length × width
= 14 cm × 6 cm
= 84 cm²
Therefore, the area of the quadrilateral ABCD is 84 square centimeters.