Area of plane figures

Advanced Math 6 · Unit 11 · area-triangles-trapezoids · Teacher edition

area-triangles-trapezoids

Name ______________________________Date ______________

1.
A triangle has base $10$ cm and height $6$ cm. What is its area in cm²?
Answer: ______________
2.
A trapezoid has parallel sides of $8$ cm and $12$ cm and a height of $5$ cm. What is its area in cm²?
Answer: ______________
3.
A parallelogram has a base of $9$ cm. Its slanted side is $5$ cm long, and the perpendicular distance between the base and the opposite side is $4$ cm. What is its area?
1. (A)
  $18$ cm²
2. (B)
  $26$ cm²
3. (C)
  $36$ cm²
4. (D)
  $45$ cm²
4.
A triangle has area $24$ cm² and base $8$ cm. What is its height in cm?
Answer: ______________
5.
A parallelogram has base $12$ cm and height $7$ cm. A triangle with base $6$ cm and height $4$ cm is cut out of it. What is the area of the remaining shaded region, in cm²?
Answer: ______________

Answer key — Area of plane figures

1.
30area-triangles-trapezoids-01
$A = \frac{1}{2} \times 10 \times 6 = \mathbf{30}$ cm².
2.
50area-triangles-trapezoids-02
$A = \frac{1}{2}(8 + 12)(5) = 10 \times 5 = \mathbf{50}$ cm².
3.
(C)
$36$ cm²
area-triangles-trapezoids-03
$A = 9 \times 4 = \mathbf{36}$ cm². ( $45$ uses the slanted side as the height; $18$ halves as if it were a triangle; $26$ is a perimeter-style sum.)
4.
6area-triangles-trapezoids-04
$\frac{1}{2} \cdot 8 \cdot h = 24 \Rightarrow 4h = 24 \Rightarrow h = \mathbf{6}$ cm.
5.
72area-triangles-trapezoids-05
Parallelogram $= 12 \times 7 = 84$ . Triangle $= \frac{1}{2} \cdot 6 \cdot 4 = 12$ . Shaded $= 84 - 12 = \mathbf{72}$ cm².