Question

Question:

Find the area of the red triangle.

need expiation and well solved solution

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Answer 1

See we need to find area of the red triangle ?

The Question will be :

ABCD is a parallelogram . In the diagram the area of yellow regions are 8 , 10 , 72 and 79. Find the area of red triangle. The diagram is not to scale.

Solution:

Red triangle area :

$79 + 10 - 72 - 8 = 9$

Do you know why triangle area is 9 ?

It's important to understand the method to verify the answer and the answer and to strengthen problem solving skills.

The key is finding a triangle or set of triangles , who's area = 1/2 the area of the parallelogram.

__________

Important steps :

1. First label the remaining areas as shown in the figure.
2. we have labeled red part as x so we know that we have to solve for x.

Solving :

The blue part will be

$= \frac{(base) \times (height)}{2}$

$= \frac{area \: of \: parallelogram}{2}$

$= (x + a) + (72 + b + 8)$

Now , let's solve for orange part

which is ,

$= \frac{(base) \times (height)}{2}$

$= \frac{area \: of \: parallelogram}{2}$

$= a + 79 + b + 10$

If we mix both the part ,

blue and orange part

which will be ,

$(x + a) + (72 + b + 8) = a + 79 + b + 10$

we will cut a and b from brackets and a and b from outside part

which will be ,

$x + 72 + 8 = 79 + 10$

So we need to solve for x

So ,

$x = 79 + 10 - 72 - 8 = 9$

Hence , the area of red part = 9