A shape is like a triangle with a flat top: its two parallel sides are 45 and 8, and the height between them is 21. Find its area.

Step-by-step solution

1. 1

   Name the shape correctly. A quadrilateral with exactly one pair of parallel sides is a trapezoid; a triangle with its apex cut off by a line parallel to the base gives exactly that. So the trapezoid area formula applies, not the triangle one.

2. 2

   Write the formula and identify the inputs. $A=\frac12(b_1+b_2)h$, where $b_1=45$ and $b_2=8$ are the parallel sides and $h=21$ is the perpendicular distance between them. The slanted sides never enter the formula.

3. 3

   Average the parallel sides. $\frac{45+8}{2}=\frac{53}{2}=26.5$. Reading the formula as average width times height makes the result easy to sanity-check.

4. 4

   Multiply by the height. $A=26.5\times 21=556.5$ square units, equivalently $\frac{1113}{2}$.

5. 5

   Sanity-check against bounding rectangles. A rectangle $8\times 21=168$ is too small and a rectangle $45\times 21=945$ is too large; $556.5$ sits between them, close to the midpoint as expected for a trapezoid.

6. 6

   Cross-check by splitting the figure. Cut the trapezoid into a rectangle $8\times 21=168$ and a triangle with base $45-8=37$ and height $21$, area $\frac12(37)(21)=388.5$. The total is $168+388.5=556.5$, matching.