A trapezoid has two right angles, and bases, and a height. Sketch the trapezoid and find its perimeter and area. Are the right angles consecutive or opposite angles? How does knowing the height help you find the perimeter?
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A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides of a trapezoid are called bases, and the nonparallel sides are called legs. The pairs of consecutive angles that include each of the bases are called base angles. Sketch a trapezoid and label the vertices T, R, A, and P. Identify the bases, legs, and both pairs of base angles.
The formula for the area A of a trapezoid is A = 1/2 h(b1 + b2), where h is the height and b1 and b2 are the lengths of the two bases. Solve the formula for b1. Justify each step. Then find the length of one of the bases of the trapezoid when the area of the trapezoid is 91 square meters, the height is 7 meters, and the length of the other base is 20 meters.
London misplaced his 14mm wrench, so he is 3D printing a replacement, just a card with a regular hexagon-shaped hole (regular means that the sides are all the same length). The 14mm of a hex wrench is the distance from one flat side to the flat side opposite; however, London’s 3D printing software requires the distance from one vertex (corner) to the opposite vertex. Draw a diagram of this scenario. Label the 14mm and the distance London needs to calculate.Find the distance that London needs for his design. Round your answer to the nearest tenth of a mm. SHOW YOUR WORK.Hint: If you connect each vertex with its opposite, then you have divided the hexagon into six triangles. What has to be true about the angles of those triangles?
