What is the area of a trapezoid that has a base length of 13 in., a base length of 7 in., and a height of 12 in.? ___ in.²
The formula for the area of a trapezoid is A = (1/2)h(b1 + b2), where h is the height of the trapezoid and b1 and b2 are the lengths of the two parallel bases.
Plugging in the values given:
A = (1/2)(12)(13 + 7)
A = (1/2)(12)(20)
A = 6 * 20
A = 120 sq. in.
Therefore, the area of the trapezoid is 120 square inches.
A trapezoid has one pair of opposite parallel sides and one pair of opposite non-parallel sides. The pair of parallel sides has lengths 15 yd. and 19 yd. The non-parallel sides have lengths of 11 yd. and 8 yd. The distance between the parallel sides is 12 yd. What is the area of the trapezoid? ___ yd.²
To find the area of the trapezoid, we first need to determine the height of the trapezoid. The height is the perpendicular distance between the two parallel sides.
We can use the Pythagorean theorem to find the height:
h^2 = 12^2 - ((19-15)/2)^2
h^2 = 144 - 2^2
h^2 = 144 - 4
h^2 = 140
h = √140
h ≈ 11.83 yd
Now, we can calculate the area of the trapezoid using the formula A = (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the two parallel bases:
A = (1/2)(15+19) * 11.83
A = (1/2)(34) * 11.83
A = 17 * 11.83
A ≈ 201.11 sq. yd
Therefore, the area of the trapezoid is approximately 201.11 square yards.
A pool company is installing a parallelogram-shaped swimming pool in a family’s backyard. Compose a rectangle to find the amount of area that the pool will take up in the yard. What is the area of the pool? ___ square feet
A parallelogram can be divided into two congruent triangles by drawing a diagonal from one vertex to the opposite side.
When you compose the parallelogram into a rectangle by moving the triangle to the opposite side, the new rectangle will have the same area as the parallelogram.
Let's assume the base of the parallelogram (pool) is the same as the base of the rectangle, and the height of the parallelogram is the same as one of the sides of the rectangle, as they are both the same length.
Given that the base of the parallelogram is the same as the base of the rectangle, and the height of the parallelogram (pool) is 12 feet (perpendicular distance between the two parallel sides), the area of the pool would be the same as the area of the rectangle.
Since the rectangle has two sides, which are also the base and the height of the pool, the area would be:
Area = base * height = base * 12 feet
Without specific measurements for the base of the parallelogram (pool), we can't provide an exact area. If you provide the length of the base, we can calculate the area of the pool for you.