Question

which figure has a greater area?
first right triangle: height 19 mm, base 36 mm; second right triangle: height 27 mm, base 22 mm
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Explanation:

Step1: Calculate area of first triangle

The formula for the area of a right - triangle is $A=\frac{1}{2}\times base\times height$. For the first triangle, base = 36 mm and height = 19 mm. So, $A_1=\frac{1}{2}\times36\times19$. First, calculate $36\times19 = 684$, then $\frac{1}{2}\times684=342$ square millimeters.

Step2: Calculate area of second triangle

For the second triangle, base = 22 mm and height = 27 mm. Using the area formula for a right - triangle $A = \frac{1}{2}\times base\times height$, we have $A_2=\frac{1}{2}\times22\times27$. First, calculate $22\times27 = 594$, then $\frac{1}{2}\times594 = 297$ square millimeters.

Step3: Compare the two areas

We compare $A_1 = 342$ and $A_2=297$. Since $342>297$, the first triangle (with base 36 mm and height 19 mm) has a greater area.

Answer:

The right - triangle with base 36 mm and height 19 mm (the first triangle) has a greater area.