Question

level 296
what is the area of the boat?
select an answer
a 625.0 cm²
b 125.8 cm
c 662.5 cm²
d 562.5 cm²

Explanation:

Step1: Calculate area of square

The square has side 10 cm. Area of square is $side^2 = 10^2 = 100$ $cm^2$.

Step2: Calculate area of trapezoid

The trapezoid has bases 35 cm and (30 + 10) = 40 cm? Wait, no, wait. Wait, the lower base is 35 cm, the upper base of the trapezoid: the horizontal segment above the trapezoid: the square is 10 cm, then the horizontal part to the right is 30 cm? Wait, no, the diagram: the boat is composed of a square (10x10) and a trapezoid. Wait, the trapezoid: the two parallel sides: the top side of the trapezoid is (10 + 30)? Wait, no, the square is 10 cm wide (since it's 10 cm on top). Then the horizontal part to the right of the square is 30 cm, so the top base of the trapezoid is 10 + 30 = 40 cm? Wait, no, the height of the trapezoid: the total height is 25 cm, minus the square's height (10 cm), so 25 - 10 = 15 cm? Wait, no, the trapezoid's height: looking at the diagram, the vertical height from the top of the trapezoid to the bottom is 25 - 10 = 15 cm? Wait, no, the trapezoid has bases: the lower base is 35 cm, the upper base: the square is 10 cm, then the horizontal segment to the right is 30 cm, so upper base is 10 + 30 = 40 cm? Wait, no, maybe I misread. Wait, the trapezoid: the two parallel sides are 35 cm (bottom) and (10 + 30) = 40 cm (top)? Wait, no, the height of the trapezoid: the vertical distance between the two bases. The total height of the boat is 25 cm, the square is 10 cm tall, so the trapezoid's height is 25 - 10 = 15 cm? Wait, but the slant side is 15.8 cm. Wait, maybe the trapezoid's height is 15 cm (since 15-8-15? Wait, no, 15.8 is the slant height. Wait, maybe the trapezoid is a right trapezoid? Wait, the left side is vertical (since there's a right angle), so the height of the trapezoid is 25 - 10 = 15 cm. Then the two parallel sides: the bottom base is 35 cm, the top base is (10 + 30) = 40 cm? Wait, no, the square is 10 cm wide (horizontal), then the horizontal part to the right is 30 cm, so the top base of the trapezoid is 10 + 30 = 40 cm? Wait, no, maybe the top base is 10 + 30 = 40 cm, bottom base 35 cm, height 15 cm. Then area of trapezoid is $\frac{(a + b)}{2} \times h = \frac{(40 + 35)}{2} \times 15$? Wait, that would be $\frac{75}{2} \times 15 = 37.5 \times 15 = 562.5$? No, that can't be. Wait, maybe I made a mistake. Wait, the square is 10x10, area 100. Then the trapezoid: the two bases are 35 cm (bottom) and 10 + 30 = 40 cm (top)? Wait, no, maybe the top base is 10 + 30 = 40? Wait, no, the horizontal segment above the trapezoid: the square is 10 cm, then the horizontal line to the right is 30 cm, so the top base of the trapezoid is 10 + 30 = 40 cm. The bottom base is 35 cm. The height of the trapezoid: the vertical distance between the two bases. The total height of the boat is 25 cm, the square is 10 cm tall, so the trapezoid's height is 25 - 10 = 15 cm. Then area of trapezoid is $\frac{(40 + 35)}{2} \times 15 = \frac{75}{2} \times 15 = 37.5 \times 15 = 562.5$? Wait, no, 37.5*15 is 562.5? Wait, 37.5*10=375, 37.5*5=187.5, total 562.5. Then the square is 10*10=100. Wait, no, that would be 562.5 + 100 = 662.5? But option C is 662.5. Wait, but maybe I messed up the trapezoid's bases. Wait, maybe the top base of the trapezoid is 30 + 10 = 40? No, wait, the square is 10 cm (width), then the horizontal part to the right is 30 cm, so the top base of the trapezoid is 10 + 30 = 40 cm. The bottom base is 35 cm. The height of the trapezoid is 25 - 10 = 15 cm. Then area of trapezoid is (40 + 35)/2 * 15 = 75/2 *15 = 37.5*15=562.5. Then the square is 10*10=100. So total area is 562.5 + 100 = 662.5? But option C is 662.5. Wait, but let's check again. Wait, maybe the trapezoid's top base is 35 cm? No, that doesn't make sense. Wait, maybe the square is 10x10, area 100. Then the trapezoid: the two bases are 35 cm (bottom) and (10 + 30) = 40 cm (top), height 15 cm. Then trapezoid area is (35 + 40)/2 *15 = 75/2 *15=562.5? No, 75/2 is 37.5, 37.5*15=562.5. Then square is 100, total 562.5 + 100=662.5, which is option C. Wait, but let's check the answer options. Option C is 662.5 cm². Wait, but maybe I made a mistake. Wait, another approach: the boat is a square (10x10) and a trapezoid. The trapezoid: bases a=35, b=10+30=40, height h=25-10=15. Area of trapezoid is (a + b)/2 * h = (35 + 40)/2 *15 = 75/2 *15=562.5. Area of square is 10*10=100. Total area 562.5 + 100=662.5, which is option C.

Answer:

C. 662.5 cm²