Answer:
Area = 1320 square meters
Explanation:
Finding the height of the trapezoid:
The height of the trapezoid is the measure of the left side of the trapezoid.
We see that the two altitudes in the trapezoid are congruent and thus they're equal.
Thus, we have one right triangle with a 10 m side, a 26 m side, and a side with an unknown length.
The Pythagorean theorem is given by:
a^2 + b^2 = c^2, where
- a and b are the triangle's shortest sides called legs,
- and c is the longest side called the hypotenuse (it's always opposite the right angle).
Thus, we can plug in 10 for a and 26 for c, allowing us to solve for b (the height of the trapezoid):
Step 1: Plug in values and simplify:
10^2 + b^2 = 26^2
100 + b^2 = 676
Step 2: Subtract 100 from both sides:
(100 + b^2 = 676) - 100
b^2 = 576
Step 3: Take the square root of both sides to solve for b:
√(b)^2 = √576
b = 24
Thus, the height of the trapezoid is 24 meters.
Finding the area of the trapezoid:
The formula for area of a trapezoid is given by:
A = 1/2(p + q)h, where
- A is the area in square meters,
- p and q are the bases of the trapezoid (top and bottom when a trapezoid is standing on one of its bases),
- and h is the height.
Step 1: Find p and q
We see that the top base is a combination of the 10 m side and the 40 m side (like the altitudes, there are also two congruent sides for the top and bottom of the trapezoid.
Thus, the entire measure of the top base (p in the trapezoid area formula) is 50 m.
Similarly, the bottom base consists of the 40m side and the 20 m side.
Thus, the entire measure of the bottom base (q in the trapezoid area formula) is 60 m as 40 + 20 = 60 m.
Step 2: Plug in values for p, q, and h in the trapezoid area formula and simplify:
Now we can plug in 50 for p, 60 for q, and 24 for h in the area formula and simplify to solve for A, the area of the trapezoid in square meters:
A = 1/2(50 + 60) * 24
A = 1/2(110) * 24
A = 55 * 24
A = 1320
Thus, the area of the trapezoid is 1320 square meters.