Question

find the missing length of the following figure if the area of the shaded region is 4 mm² and write your result in the empty box.
figure with a right angle, 2 mm height, and length z for the shaded triangles base
answer: empty box mm.

Explanation:

Step1: Recall triangle area formula

The area of a triangle is $A = \frac{1}{2} \times b \times h$, where $b$ is the base (length $z$) and $h$ is the height (2 mm).

Step2: Substitute known values

Substitute $A=4$ mm² and $h=2$ mm into the formula:
$4 = \frac{1}{2} \times z \times 2$

Step3: Simplify and solve for $z$

Simplify the right-hand side: $\frac{1}{2} \times 2 = 1$, so $4 = 1 \times z$, which gives $z=4$.

Answer:

4