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# Area of Triangle - Box Method

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 Sub Topics A packed or closed shape which contains three lines linked end to end is known as triangle. It is a kind of Polygon. There are different properties which are given below: Three corner points are present in a triangle and the corner Point is known as vertex of a triangle. Now we will see how to find the Area of Triangle Box Method? In box method triangle is drawn in a box and that box contains small number if rectangles with the help of which we can find the area of triangle. Now we will see some steps for finding the area of triangle by using box method: Step 1: First we have a box and the triangle is present inside the box. Step 2: Then we find the area of the box. Step 3: Then we add all sides of a triangle and then subtract from the area of the box. Step 4: On subtracting the values from the area of box we get area of triangle. When we subtract the area of a simple shape which is present inside the box then we get the area of triangle. Suppose we have the area of the box which is 1500, and the length of each sides inside the triangle is 100, 225 and 725 inch; then find the area of triangle by using the box method; We know that when we subtract sides of triangle from the area of a box then we get triangle area; So the area of box is 1500; And each side of a triangle is 100, 225 and 725; So the area of triangle is: => 1500 – 100 – 225 – 725; => 1500 – 1050; => 450 inch2 So the area of triangle by using box method is 450 inch2.

## When One Vertex is Inside the Box

In Geometry we study different types of cases and one of them is “when one Vertex is inside the box”. Let us take a rectangular box, in rectangular box a triangle is present in which one vertex of a triangle is inside a box and if we want to find the area then we simply subtract the area of Rectangle from the three Triangles which are present inside the box.

We can calculate the Area of Triangle when one Vertex is inside the box by following steps shown below:

Step 1: To find area first we have to draw a rectangular box and this box is just like an orthogonal rectangle. A rectangle which has all four sides either vertical or horizontal is known as orthogonal rectangle.

Step 2: The rectangle is enclosed by the triangle. Now we will calculate the area of box.

Step 3: Now find the area of the three right triangles which are formed in box. Here we use half base time method to find the area.

Step 4: The formula for finding the area of triangle is given by:

Area of triangle = $\frac{1}{2}$ ab

Where ‘b’ denotes the length of base, and ‘a’ denotes the length of corresponding Altitude;

Step 5: If one of the vertices of a triangle is inside the box then we can calculate the area of small rectangle which is formed in the corner.

The formula for finding the area of rectangle is given by:

Area of rectangle = wh;

Where, ‘w’ denotes the width and ‘h’ is the height of a rectangle.

Step 6: At last subtract the area of three triangles from the area of the rectangular box; it will give us the area of triangle.
This is the process of finding area when one Vertex is inside the box.