Question

Here are two triangles identical in size.10 cm.The two triangles are overlapped 3 cm 6 cm.What is the area of the blue triangle showing?


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Answer 1

Answer:

51 cm²

Step-by-step explanation:

Let's ASSUME that the vertical measurements are taken perpendicular to the roughly horizontal baselines.

The three yellow triangles are all similar

the upper small triangle has height 3 and base 6 cm. The ratio of the lengths is 6/3 = 2

This means the medium (overlapping) triangle has lengths 10 - 3 = 7 and 7(2) = 14 cm

Area of the large triangle is ½(14 + 6)(10) = 100 cm²

Area of the overlapping yellow triangle is ½(7)(14) = 49 cm²

Exposed area of the blue triangle is 100 - 49 = 51 cm²

Answer 2

Both triangles have an area of 100 square centimeters and the area of the blue triangle showing is 51 square centimeters.

Based on the information given from statement, we can determine the missing length of the yellow triangle by means of simmilarity ratios, that is:

$\frac{3\,cm}{6\,cm} = \frac{10\,cm}{x}$ (1)

Where $x$ is the base of the yellow triangle, in centimeters.

Now we proceed to find the length base:

$x = \frac{6\,cm}{3\,cm}\times 10\,cm$

$x = 20\,cm$

The area of the triangle can be found by means of the following expression:

$A = \frac{1}{2}\cdot b\cdot h$ (2)

Where:

• $A$ - Area of the yellow triangle, in square centimeters.
• $b$ - Base, in centimeters.
• $h$ - Height, in centimeters.

If we know that $b = 20\,cm$ and $h = 10\,cm$, then the area of the triangle is:

$A = \frac{1}{2}\cdot (20\,cm)\cdot (10\,cm)$

$A = 100\,cm^{2}$

The area of the yellow triangle is 100 square centimeters and the area of the blue triangle is also 100 square centimeters due to congruency. The dimensions of the section of the yellow triangle overlapping the blue triangle are $b = 14\,cm$ and $h = 7\,cm$. The area of this section is:

$A' = \frac{1}{2}\cdot (14\,cm)\cdot (7\,cm)$

$A' = 49\,cm^{2}$

And the area of the rest of the blue triangle is:

$A'' = A - A'$ (2)

$A'' = 100\,cm^{2}-49\,cm^{2}$

$A'' = 51\,cm^{2}$

In a nutshell, both triangles have an area of 100 square centimeters and the area of the blue triangle showing is 51 square centimeters.

We kindly invite to check this question on triangles: https://brainly.com/question/23103213