Find the area of the triangle. The drawing is not to scale. Please round your answer to the nearest tenth and show all work.
the legs of the triangle are both 30 cm, while the base is 26 cm.
To find the area of the triangle, we can use the formula:
Area = 0.5 * base * height
In this case, the base is 26 cm and the height is one of the legs, which is 30 cm.
Area = 0.5 * 26 * 30
Area = 0.5 * 780
Area = 390 square centimeters
Therefore, the area of the triangle is 390 square centimeters.
The area of a triangle is 132 square units. What would its new area be if its base was half as long and its height was three times as long? Please show all work to receive full credit.
Let the original base of the triangle be b units and the original height be h units.
The area of the original triangle can be expressed as:
Area = 0.5 * base * height
132 = 0.5 * b * h
Since the new base is half as long and the new height is three times as long, the new base is b/2 units and the new height is 3h units.
The area of the new triangle can be expressed as:
New Area = 0.5 * new base * new height
New Area = 0.5 * (b/2) * (3h)
New Area = 0.5 * 3/2 * b * 3h
New Area = 0.75 * b * 3h
New Area = 2.25 * b * h
We know that the original area is 132 square units:
132 = 0.5 * b * h
b * h = 264
Substitute this value into the equation for the new area:
New Area = 2.25 * 264
New Area = 594 square units
Therefore, the new area of the triangle would be 594 square units.
There are three different sectors of a circle. Sector A has a measure of 0.5 %, sector B has a measure of 0.15 %, and sector C has a measure of 0.35 %. What is the degree measure of sector B? Please show work.
To find the degree measure of sector B, we need to first convert the percentage measures to degrees because a percentage is a fractional part of 100%.
We know that a complete circle has 360 degrees.
For sector A:
0.5% of the circle = 0.5/100 * 360 = 1.8 degrees
For sector B:
0.15% of the circle = 0.15/100 * 360 = 0.54 degrees
For sector C:
0.35% of the circle = 0.35/100 * 360 = 1.26 degrees
Therefore, the degree measure of sector B is 0.54 degrees.