Answer:
The area of ∆DEF = 4.5in²
Step-by-step explanation:
From the above diagram,
∆BAC ~∆DEF
It is important to note that if two triangles are similar, the ratio of their areas is equal or equivalent to the ratio of the areas of their sides
This means for the above question, that
We have the bigger triangle = ∆BAC has a side of 4 in and Area = 8 in²
The small triangle has a side of 3in
Finding the scale factor k = ratio of the sides of both Triangles
k = 4/3
k² = (4/3)²
k² = 16/9
Hence,
Area of ∆BAC/ Area of ∆DEF = 16/9
8in²/Area of ∆DEF = 16/9
We cross Multiply
8 in² × 9 = Area of ∆DEF × 16
Divide both sides by 16
Area of ∆DEF = 72/16
= 4.5in²
Therefore, the Area of ∆DEF rounded to the nearest tenth = 4.5in²
A reasonable estimate is like 8 or 9 or maybe even 10
hope this helps
Answer:
∠DEF = 250°
Step-by-step explanation:
1. This shape is a hexagon (6 sides), so the interior angles should all add to 720°. Also worth noting: the problem says the <em>obtuse</em> angle DEF; this means it's the angle INSIDE the shape, not outside.
2. Add all the known angles, then subtract from the total degrees:
50 + 96 + 144 + 42 = 332
720 - 332 = 338
3. Because BC is parallel to ED, we can subtract 180 - 42 for the value of ∠EDC, which is 138°.
4. Add all the known values and subtract from 720 for the value of ∠DEF:
50 + 96 + 144 + 42 + 138 = 470
720 - 470 = 250°
Step-by-step explanation:
