Question

What is the area of triangle BCD to the nearest tenth of a square centimeter? Use special right triangles to help find the height. Show your work!!!

Answer 1

Answer:

$31.2$ $cm^2$

Step-by-step explanation:

To find the area, you first need the measure of the other leg, AB. We know two angles, one of 90° and the other of 60°. Since a triangles angles will always add up to a total of 180°, we can conclude that the other angle is 30°. You can use the 30°-60°-90° theorem:

$longer$ $leg=\sqrt{3}*shorter$ $leg$

Insert the values. Let $l$ be AB:

$l=\sqrt{3}*6$

Simplify:

$l=6\sqrt{3}$

The length of AB is $6\sqrt{3}$.

Use this to find the area:

$A=\frac{ab}{2}$

a and b are the legs, as in the Pythagorean theorem. Insert the values:

$A=\frac{6*6\sqrt{3} }{2}$

Simplify multiplication:

$A=\frac{36\sqrt{3}}{2}$

Simplify division:

$A=18\sqrt{3}$

Convert to decimal:

$A=31.18$

Round to the nearest tenth:

$A=31.2$

The triangle has an area of $31.2$ $cm^2$.

Finito.

Answer 2

Answer:

2.7 cm2

Step-by-step explanation:

We have been given an image of a 30-60-90 triangle. We are asked to find the area of our given triangle.First of all, we need to find the height of our given triangle.In a 30-60-90 triangle, the shorter leg that corresponds to 30 degree angle is  units long. The sides corresponding to 60 and 90 degree angles are  and  respectively.Since the value of  is 5 cm, so the height of our given triangle (corresponding to 60 degree angle) will be:Upon substituting our given values in area of triangle formula we will get,Therefore, the area of our given triangle is 21.7 square centimeters.