Find the area of the triangle.
A triangle is shown. The base of the triangle is labeled 34 yards. At approximately the center of this base, a vertical dashed line segment is drawn to the opposite vertex. A small square is located at the intersection of the dashed line with the side of the triangle. The dashed line segment is labeled 6.3 yards.
A. 107.1 yd2
B. 214.2 yd2
C. 306.8 yd2
D. 410.3 yd2
3 answers
We can use the formula for the area of a triangle: $$\text{Area} = \frac{1}{2}(\text{base})(\text{height}).$$ We know the base is 34 yards. To find the height, we can use the dashed line segment of length 6.3 yards as one leg of a right triangle, with the height of the triangle as the other leg. The hypotenuse of this triangle is the same as the height of the entire triangle. We can use the Pythagorean Theorem to find the height: $$\text{height} = \sqrt{\text{hypotenuse}^2 - \text{leg}^2} = \sqrt{34^2 - 6.3^2} \approx 33.9 \text{ yards}.$$ Plugging in the values for base and height, we get: $$\text{Area} = \frac{1}{2}(34\text{ yd})(33.9\text{ yd}) \approx 577.3\text{ yd}^2.$$ Rounded to one decimal place, this is: $$\boxed{\textbf{(B)}\ 214.2\text{ yd}^2}.$$
wha- there aint no way thas english
I apologize if my previous response was difficult to understand. Here is another explanation:
We are given a triangle with a base of length 34 yards and a dashed line segment of length 6.3 yards drawn to the opposite vertex. A small square is located at the intersection of the dashed line with the side of the triangle. We need to find the area of the triangle.
One way to find the area of the triangle is to use the formula: $$\text{Area} = \frac{1}{2}(\text{base})(\text{height})$$ where the base is 34 yards and the height is the length of the dashed line segment.
To find the length of the height, we can use the Pythagorean Theorem. If we draw a perpendicular line from the opposite vertex to the base of the triangle, it splits the triangle into two right triangles. The length of the dashed line segment is one leg of one of these triangles, and the height of the triangle is the length of the other leg. We can use the Pythagorean Theorem to find the length of the height:
$$\text{height} = \sqrt{\text{hypotenuse}^2 - \text{leg}^2}$$
The hypotenuse is the height of the entire triangle, and we can find it using the Pythagorean Theorem again:
$$\text{hypotenuse} = \sqrt{(\text{base}/2)^2 + (\text{dashed line}/2)^2} = \sqrt{(34/2)^2 + (6.3/2)^2} \approx 33.9\text{ yards}$$
Substituting this value into the first formula, we get:
$$\text{Area} = \frac{1}{2}(34\text{ yd})(33.9\text{ yd}) \approx 577.3\text{ yd}^2$$
Rounded to one decimal place, this is:
$$\boxed{\textbf{(B)}\ 214.2\text{ yd}^2}.$$
We are given a triangle with a base of length 34 yards and a dashed line segment of length 6.3 yards drawn to the opposite vertex. A small square is located at the intersection of the dashed line with the side of the triangle. We need to find the area of the triangle.
One way to find the area of the triangle is to use the formula: $$\text{Area} = \frac{1}{2}(\text{base})(\text{height})$$ where the base is 34 yards and the height is the length of the dashed line segment.
To find the length of the height, we can use the Pythagorean Theorem. If we draw a perpendicular line from the opposite vertex to the base of the triangle, it splits the triangle into two right triangles. The length of the dashed line segment is one leg of one of these triangles, and the height of the triangle is the length of the other leg. We can use the Pythagorean Theorem to find the length of the height:
$$\text{height} = \sqrt{\text{hypotenuse}^2 - \text{leg}^2}$$
The hypotenuse is the height of the entire triangle, and we can find it using the Pythagorean Theorem again:
$$\text{hypotenuse} = \sqrt{(\text{base}/2)^2 + (\text{dashed line}/2)^2} = \sqrt{(34/2)^2 + (6.3/2)^2} \approx 33.9\text{ yards}$$
Substituting this value into the first formula, we get:
$$\text{Area} = \frac{1}{2}(34\text{ yd})(33.9\text{ yd}) \approx 577.3\text{ yd}^2$$
Rounded to one decimal place, this is:
$$\boxed{\textbf{(B)}\ 214.2\text{ yd}^2}.$$
1 answer