Question

which figure has a greater area?
first triangle: base 36 ft, height 19 ft (dashed line, right angle symbol at base and height intersection)
second triangle: leg 24 ft (vertical), leg 30 ft (horizontal), right angle symbol at their intersection
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Explanation:

Step1: Calculate area of first triangle

The formula for the area of a triangle is $A = \frac{1}{2} \times base \times height$. For the first triangle, base = 36 ft, height = 19 ft. So area $A_1 = \frac{1}{2} \times 36 \times 19$.
$A_1 = 18 \times 19 = 342$ square feet.

Step2: Calculate area of second triangle

For the second triangle, base = 30 ft, height = 24 ft. Using the same formula, area $A_2 = \frac{1}{2} \times 30 \times 24$.
$A_2 = 15 \times 24 = 360$ square feet.

Step3: Compare the two areas

Compare $A_1 = 342$ and $A_2 = 360$. Since $360 > 342$, the second triangle (with base 30 ft and height 24 ft) has a greater area.

Answer:

The right - angled triangle with base 30 ft and height 24 ft (the second triangle) has a greater area.