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MAT 136 Exam 2 | Actual Questions and Answers Latest Updated 2024/2025 (Graded A+)
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MAT 136 Exam 2 | Actual Questions and Answers Latest Updated 2024/2025 (Graded A+)
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MAT 136 Exam 2 | Actual Questions and Answers Latest Updated 2024/2025 (GradedA+)
The "Discovery Approach" for determining the area of a triangle. (The children
already have learned to find the area of a parallelogram.) - ✔✔a) Cut out a cardboard parallelogram in
which each base is labeled b. b) In the interior of the parallelogram, draw the height (labeled h) with
one endpoint at
a parallelogram vertex. c) In the interior of the parallelogram, draw the diagonal that does not intersect
the
height already drawn.
d) Cut on this diagonal. e) Rotate one resulting triangle and place it exactly on top of the other triangle
to
show the children that you now have formed 2 identical (congruent) triangles.
f) Say that since the area of the parallelogram was b x h, and the triangle's area is one-half the area of
the parallelogram, then the area of the triangle is
x b x h.
Also, when you know only the lengths of the triangle's 3 sides:
Heron's Formula: A = √s(s-a)(s-b)(s-c) where s = (a+b+c) / 2
The "Discovery Approach" for determining the area of a trapezoid. (The children
already have learned to find the area of a parallelogram.) - ✔✔a) Cut out two cardboard non-
isosceles trapezoids.
b) On one of the trapezoids, label the bases a and b, and the height h.
c) Rotate the second trapezoid and place it beside the first one, forming a
parallelogram. (Label the bases on this second trapezoid so that a and b correspond to the a and
b lengths shown on the first trapezoid.)
d) State that the base of the resulting parallelogram has length a + b . e) Explain that since the area of a
parallelogram equals base x height, we know that
in our parallelogram, A = (a + b) x h .
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