Given \( A=\frac{1}{2}\left(b_{1}+b_{2}\right) h \), solve for \( h \) A \( h=2 A\left(b_{1}+b_{2}\right) \) B \( \mathrm{h}=\frac{b_{1}+b_{2}}{2 A} \) C \( \mathrm{h}=\frac{2 A}{b_{1}+b_{2}} \) D \( h=A-\frac{1}{2}\left(b_{1}+b_{2}\right) \)

To solve for \( h \) in the equation \( A = \frac{1}{2}\left(b_{1}+b_{2}\right) h \), we can first rearrange the formula by isolating \( h \): Starting from: \[ A = \frac{1}{2}\left(b_{1}+b_{2}\right) h \] Multiplying both sides by \( 2 \): \[ 2A = (b_{1}+b_{2}) h \] Then, dividing both sides by \( (b_{1}+b_{2}) \): \[ h = \frac{2A}{b_{1}+b_{2}} \] So, the correct answer is C: \( h = \frac{2 A}{b_{1}+b_{2}} \). Now, let's add some fun facts: In ancient times, Egyptians and Greeks utilized the concept of area to construct amazing architectural feats like pyramids and temples. They intuitively understood how to calculate areas of various shapes long before formal algebra was developed, proving that math has been a foundational tool for humans for millennia! In the real world, knowing how to manipulate equations to solve for a variable like height can be incredibly useful, especially in fields such as civil engineering, architecture, and even landscaping. Whether you’re figuring out how much soil to fill a trapezoidal garden bed or determining the dimensions for a unique roof design, these skills come in handy!