Question: User: Name:
Date:
Period:
7. Find the area of the triangle:
60°
60°
4\sqrt{15} = h
P=5+5+5
A = 1/2 b\cdot h
4\sqrt{15}/\sqrt{3} = 4\sqrt{5}
x
4\sqrt{5} \times 2
8\sqrt{5}
1/2(8\sqrt{5} \times 4\sqrt{15})
8. Find the perimeter of the square:
28
90
90
90
45°
45°
45°
45°
u^2
9. Steel loading ramps are used to load a
lawn mower onto a truck bed that is 37.5
inches above the ground. If each ramp
makes a 30° angle with the ground, find
the length of the ramp in inches.
10. The infield of a baseball field is shaped
like a square with each side measuring 90
feet. A player throws the ball from third
base to first base, which are located at
opposite corners of the square. Find the
distance the ball travels from third base to
first base.
top-left: triangle with base angles 60° and a dashed altitude labeled h = 4\sqrt{15}; this is an equilateral-triangle area problem.
top-right: square with diagonal labeled 28, perimeter sought; right-angle corners shown and diagonal runs from top-left to bottom-right.
1. **Problem:** Find the area of the equilateral triangle with side length $5$ and altitude $h = 4\sqrt{15}$.
2. **Formula:** The area $A$ of a triangle is given by $$A = \frac{1}{2} \times \text{base} \times \text{height}.$$
3. Since the triangle is equilateral with side length $5$, the base $b = 5$. The altitude $h$ is given as $4\sqrt{15}$.
4. Calculate the area:
$$A = \frac{1}{2} \times 5 \times 4\sqrt{15} = \frac{1}{2} \times 20\sqrt{15} = 10\sqrt{15}.$$
5. **Simplify the altitude:** The altitude can also be found by the formula for an equilateral triangle altitude:
$$h = \frac{\sqrt{3}}{2} \times 5 = \frac{5\sqrt{3}}{2}.$$
6. The given altitude $4\sqrt{15}$ is consistent with the problem statement, so we use it directly.
7. **Final answer:** The area of the triangle is $$\boxed{10\sqrt{15}}.$$