Respuesta :

Answer:  A) 45 square cm

============================================================

Explanation:

The length of 17 cm and slanted length of 10 cm are not used at all. They are likely thrown in as a distraction.

Instead, we focus on the horizontal base of 10 cm and the vertical height of 9 cm. The base and height are always perpendicular to one another.

The area of the triangle is therefore...

area = base*height/2

area = 10*9/2

area = 90/2

area = 45 square cm

It doesn't matter that this triangle is obtuse, the same area formula applies to any triangle.

------------

A longer method would have you compute the area of the dashed triangle, and the area of the two combined triangles (the largest overall triangle). Subtracting the two would lead to the answer of 45 cm^2. You'll need the pythagorean theorem to find the base of the dashed triangle, which then helps find the base of the largest triangle overall as well. At this point is when the 17 and 10 come into play, but I find the first method is much easier.

breadsticksandcheese

Answer:

C. 50 [tex]cm^2[/tex]

Step-by-step explanation:

area of big triangle - area of small triangle

find missing side lengths with pythagorean theorem:

[tex]9^2 + b^2=10^2\\\\81+b^2=100\\\\b^2= 19\\\\b=\sqrt{19}\\[/tex]

[tex]10^2+b^2=17^2\\\\100+b^2=289\\\\b^2=189\\\\b=\sqrt{189}[/tex]

find area:

1/2(10)([tex]\sqrt{189}[/tex] ) - 1/2([tex]\sqrt{19}[/tex] )(9)

=   49.124

which is closest to 50 [tex]cm^2[/tex]

Otras preguntas