7th grade math, 15 points
2 answers:
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Answer:
Perimeter of ΔABC: +
units
Area of ΔABC: units
<u>Skills required: HS Geo, Special Triangles</u>
Step-by-step explanation:
1) The best option is to break down this triangle. Let's draw an altitude from Point B down to Segment AC. The point from the altitude that intersects AC is Point D. BD is the height of our triangle, AC is the base.
2) Angle A is 60 degrees, and since Angle BDA is 90 degrees, Angle ABD is 30 degrees. We can use the 30-60-90 degree right triangle property for the triangle BDA.
- This states that if the side opposite the 30 degree angle is
, the side opposite the 60 degree angle is
, and the side opposite the 90 degree angle is
.
AB is 9 units, and it is opposite the 90 degree angle. This means that ==> This then means that AD, the segment opposite the 30 degree angle in this triangle is
units. Segment BD (the height) is
.
3) Angle C is 45 degrees, and Angle BDC is 90 degrees, which means that Angle CBD is 45 degrees. We can use the 45-45-90 degree right triangle property for the triangle BCD.
- This states that if the side opposite the 45 degree angle is
.
BD is , which means DC is the same. BC, which is the hypotenuse is BD multiplied by square-root-2, which is
.
4) Area is , the base (b) is AC (which is
), the height is BD (
). When multiple you will get
, then this multiplied by 1/2 is
<--> this is the area!
5) Perimeter is just the sum of all side: 9 + +
=
+
unit
