Trying to solve the area of a triangle - The Learning Company Achieve! Math & Science Grades 1-3 (381933) for PC, Mac

I find the easiest way to solve these is to sketch them first (I'm a visual learner;) We get a nice right-angled triangle, with the right-angle at B. The formula for the area of a triangle is 1/2 * base* height or (base * height)/2.

We can use BC or AB as the base.

If we use BC as the base, the length is 9-4 or 5. The height is 6-2 or 4.

We can now but the base and the height in the formula to figure out the area.

Good luck.

Paul

In two similar triangles, the ratio of their areas is the square of the ratio of their sides. Let's assume LMN and FGH are similar triangles. The ratio of the areas of LMN to FGH is 18 to 24, or 3 to 4 or 0.75. We would then take the square root of 0.75 to get the ratio of the sides. I get 0.866. The reason it is the square is the area of a triangle is base times height divided by 2, and the base and height and sides of similar triangles are proportional.

Good luck.

Paul

Similar Triangles ratio of areas

720.

Here is how i did it (my way).
1. doubled the area to 160 and found two sides of a square that would equal the area (a*b). I chose the numbers 16 (which I will use for the base of my triangle and 10 for the height.
2. Checking my answer, (h*b)/2 I see that my triangle area is indeed 80
3. multiply the base *3 = 48 and height *3 = 30
4. (30*48) / 2=720
5. Work check using calculated area of a square 3x larger: (a*b)=area (48*30) = 1440 1/2 of the area creates a triangle so: (1440/2) = 720
This may not be common core or whatever is being taught now, but having a basic knowledge of geometry allows me to figure out problems like these pretty easily.

A pyramid has 5 sides including the base. If the base is a rectangle L long and W wide, its area is L*W.

The other sides are triangles. If the height of the pyramid is H, the triangles that are L wide at the base will have a height of the square root of half of W squared plus H squared, or SQRT((.5*W)^2+H^2) and the two that are W wide at the base will have a height of SQRT((.5*L)^2+H^2). The area of a triangle is .5*height*base, so the total surface two triangles with the same height and base is 2*.5*height*base = height*base.

So, the total surface area of a pyramid L long by W wide by H tall would be:
L*W (the area of the base)
+ L*SQRT((.5*W)^2+H^2) (the area of the 2 triangles with base L)
+ W*SQRT((.5*L)^2+H^2) (the area of the 2 triangles with base W)

Hope this is helpful!

Here is to get you started. To increase the size of the image do a CTRL Plus (+) in your browser.
You need to calculate the slant height of the pyramid for the formula of the lateral area. You should find a value of (1/2)*SQRT(203) or about 7.1239 cm



You need to calculate the altitude (height) of the pyramid from the apex (summit) to the center of the base triangle (center of inscribed circle, barycenter, orthocenter). The hypotenuse of such triangle is the slant height. One leg is the altitude (to be found), the measure of the second leg is (1/3) the altitude of the equilateral triangle that forms the base. You should find (1/3) m MH= (1/3)* (11/2)*SQRT(3)


1. Calculate the area of the base (use a formula for the equilateral triangle or the general formula for a triangle: you have its height MH ).
2. Lateral area = 3 times the area of triangle Triangle ECD (in yellow above).
3. Total area = area of base + lateral area.
4. Volume= (1/3)(Area of base)* (height of pyramid)
If you can see the details on the screen capture below, fine, Press CTRL + in your browser to increase the size.

Use the formula for the area of the triangle with symbols.
Let b be the measure of the base, and h the measure of the height.
The area of the triangle is A= b*h/2 (original situation)
Now consider the new situation (situation2)
Let b` the new base and h`the new height.
We have b'=2b, and h`=h/2
The new area A`=b`*h`/2=(2b)*(h/2)/2=b*h/2 and that is equal to the original situation.
Now consider a third situation
Let b"=2b, h"=h
A"=b"*h"/2=(2b)*h/2=2(b*h/2)=2A

o find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that aparallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.
Since the area of a parallelogram is , the area of a triangle must be one-half the area of a parallelogram. Thus, the formula for the area of a triangle is: or where is the base, is the height and · means multiply. The base and height of a triangle must be perpendicular to each other. In each of the examples below, the base is a side of the triangle. However, depending on the triangle, the height may or may not be a side of the triangle. For example, in the right triangle in Example 2, the height is a side of the triangle since it is perpendicular to the base. In the triangles in Examples 1 and 3, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height.

Hi nanaeden

Use the formula depending on what is given
If one side and vertical height from that side to the opposite vertex is given, use the formula 1/2 of basexheight
If 3 sides of the triangle are given use the formula
sq root of [ s(s-a)(s-b)(s-c)] where a,b, c are the 3 sides and s is semi- perimeter.
Familiarise with formulae to solve Maths problems.
If it is helpful, please give a rating.
Have a nice day
luciana44

Hello,

1. This lot does not have the form or a regular quadrilateral (rectangle, square, parallelogram, etc.)
   
2. So you cannot calculate its area, you have to know exactly the shape it has.
3. With polygons, one usually cuts them into triangles.
   
4. You have to cut it into two triangles,
   
5. measure the base and the height of each triangle,
   
6. use the area formula for the triangle ( area = heightX base/2)
   
7. After you calculate the areas of both triangles, you add them to get the area of the the whole lot in ft^2.
   
8. Using the conversion formula between acres and ft^2 which is 1 acre=43560 ft^2, you divide the area of the lot in square feet by the number 43560 ft^2 and express the result as a percentage or a fraction .

Hope it helps.
Thanks for using FixYa.