What is the area of triangle $STV$?

In summary, the problem involves finding the area of triangle $STV$ where $UX=XY=YT$ and $UV=VS$ and the area of triangle $XVU$ is given. By using the fact that triangles with equal bases and heights have equal areas, the area of $STV$ can be found by multiplying the area of $UVX$ by 3, which results in an area of $42cm^2$.
  • #1
anemone
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MHB
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Hi all, I happened to see this primary 6 math geometry problem and thought it was a fun (not straightforward but not too hard) problem. Try it and post your solution if you are interested. (Cool)

In the figure, not drawn to scale, $UX=XY=YT$ and $UV=VS$. Given that the area of triangle $XVU$ is 14 cm$^2$, find the area of triangle $STV$.
[TIKZ]
\coordinate[label=left:U] (U) at (0,0);
\coordinate[label=right:T] (T) at (12, 0);
\coordinate[label=below: X] (X) at (4,0);
\coordinate[label=below: Y] (Y) at (8,0);
\coordinate[label=above: V] (V) at (2,1);
\coordinate[label=above:S] (S) at (4,2);
\coordinate[label=above: W] (W) at (7.2,0.4);
\draw (S) -- (U)-- (T)-- (S);
\draw (V) -- (X);
\draw (S) -- (Y);
\draw (V) -- (T);
[/TIKZ]
 
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  • #2
Area of $\triangle STV$ = area of $\triangle UVT$

because they are on equal base and same base

now area of $\triangle UVT$ is 3 times area of $\triangle UVX$

as height is same and base is 3 times

so area of $\triangle STV$ = 3 * area of $\triangle UVX$ = $42cm^2$
 

What is the formula for finding the area of a triangle?

The formula for finding the area of a triangle is A = 1/2 * base * height, where A represents the area, base represents the length of the triangle's base, and height represents the height of the triangle.

What units are used to measure the area of a triangle?

The area of a triangle is typically measured in square units, such as square inches, square feet, or square meters.

Can the area of a triangle be negative?

No, the area of a triangle cannot be negative. It is always a positive value, representing the amount of space inside the triangle.

What is the difference between finding the area of a right triangle and a non-right triangle?

The formula for finding the area of a right triangle is the same as the general formula (A = 1/2 * base * height). However, for non-right triangles, you may need to use other methods such as Heron's formula or splitting the triangle into smaller right triangles to find the area.

Can the area of a triangle be found if only the side lengths are known?

Yes, the area of a triangle can be found if the side lengths are known. You can use Heron's formula, which involves using all three side lengths, or you can split the triangle into two right triangles and use the Pythagorean theorem to find the height.

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