Greetings, and welcome to the next section of Geometry for Novices! Today, we’ll learn how to calculate the area of a triangle. This article assumes that you are familiar with two prerequisite subjects: calculating the size of a rectangle and realizing that area is measured in squares, resulting in units like square inches and square feet. If you are having trouble grasping either of these concepts, reading the related topics in the Geometry for Beginners series is recommended. Like Algebra, Geometry is a subject that constructs upon prior learning. New information cannot be understood or learned efficiently without background knowledge.
We can go on to finding the area of triangles if you already know the formula for the size of a rectangle (in both symbols and English) and have a firm grasp of why the area is measured in square units. While it is true that we will be calculating the site of a triangle, I feel it is important to note that triangles come in a wide variety of shapes and sizes. Although rectangles can have various forms, the formula A = bh always works for them because one side is always the base, and the other is always the height. Due to the enormous variety of triangle shapes, certain cases will need to be considered. However, this is the ONLY formula for calculating the area of a triangle in Geometry, so it should be easy to memorize. That’s fantastic news. The peak’s new placement is the key difference. This is where things can get complicated.
We need a rectangle diagram to get the formula for the area of a triangle. Make sure to make it big enough to name the base with “base clearly” and the sign b, and the perpendicular side with “height” and the symbol h. The area formula should be written in English and symbols and placed next to your diagram. As the saying goes, “Area is equal to base times height,” or A = bh.
I’d like you to add one of the rectangle’s diagonals to your diagram. A diagonal joins the two opposite corners of a rectangle. Can you see how the diagonal split the triangle in half? Since each triangle represents half of the rectangle, calculating their combined area is a breeze. A rectangle with sides of 6 inches and 8 inches would have a size of A = bh = 6 x 8 = 48 square inches. Since each triangle is 24 square inches, we can use the following calculation to get the total surface area of all three: A = 1/2 bh. (Note that using A for a room without specifying the type of number being discussed can lead to misunderstandings. Sometimes a little illustration is used in the subscript to help with this. In this case, the subscript number for the area of a triangle may be expressed as A, with a little triangle drawn to the right of the A. I can’t do that right now, but I think you get the idea.
This means in the language that a triangle’s area is equal to half the product of its base and height. The size of a triangle can be calculated quickly by dividing the ground by the size. A = 0.5 bh in symbol form.
Caution! Caution! Caution! Right about now is when you need to pay the closest attention. Remember that while right angles are present in all rectangles, they are not in all triangles. In a right-angle triangle, the leg opposite the tip is the base, and the portion adjacent to the rise is the height. But suppose there is no 90-degree corner.
I want you to imagine that you put some sticks together to form a rectangle to solve the “no right angle” problem. If you have ever attempted anything like this, you know that the rectangle begins to slant and the right angles begin to disappear without the use of some additional support pieces. You get a parallelogram if you make the opposite sides of your rectangle and the opposite angles the same. For example, a parallelogram is a “special case” of a rectangle. FOCUS RIGHT HERE AND NOW. When we tilt our rectangle further and more to one side by pressing on its upper corner, we see that its base maintains the same length, but its height decreases. Our original 6-inch by 8-inch rectangle is now an asymmetrical parallelogram with the same 8-inch base but a different 6-inch side serving as the new height. As one alters their altitude, so does their landmass. When did 6 inches stop being the standard?
Your memory serves me well if I assume you recall that height is always measured from the highest point directly down to the ground. No clear height line can be seen at this time. We “drop a perpendicular” line from the peak to the bottom. What this entails is merely the drawing of a straight line. The height of the parallelogram corresponds to the length of this new line. The area formula remains the same, A = bh, but we must be cautious in selecting the appropriate length as height. The size is NOT a side in a parallelogram with no right angle.
A parallelogram can be divided into two equal triangles by drawing a diagonal, just like a rectangle can be divided into two similar triangles by doing the same thing. That’s why A = 1/2 bh is still the formula for calculating the area of any triangle. Again, though, we need to be wary about whose height measurement we use.
Create a triangle that is not correct on your paper. Put “base” and a b next to the bottom side. Find the peak, and then draw a straight line to the bottom. In the new bar, write “height” followed by an h. At the moment, the height is required to calculate the area of an issue. Without being told, we cannot know how tall anything is. For the time being, keep in mind:
The formula for the area of a triangle is A = 1/2 bh, where b and h are the base and height, respectively.
Shirley Slick, aka “The Slick Tips Lady,” is a retired high school math teacher and tutor specializing in brain-based learning and teaching and holds degrees in mathematics and psychology. She hopes, first, to assist parents in assisting their children with mathematics, second, to aid in eliminating the dreadful Algebra failure rate, and third, to educate the public about challenges plaguing the area of education. To get a copy of her free report, “10 Slick Tips for Improving Your Child’s Study Habits,” go to her website.
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