Question

What is the area, in square units, of a trapezoid bounded by the lines $y = x$, $y = 10$, $y = 5$ and the $y$-axis? express your answer as a decimal to the nearest tenth

Answer 1

The area of a trapezoid is bounded by the lines y = x, y = 10, y = 5, and the y− axis is 37.5 square units.

What is the area of the trapezium?

A trapezium is a quadrilateral having two opposite sides parallel.

The area of a trapezium is equal to;

$\rm Area =\dfrac{1}{2} \times \text{Distance between the parallel sides} \times \text{Sum of the parallel sides}$

The trapezoid is bounded by the lines y = x, y = 10, y = 5, and the y− axis.

The vertices are at (0,10), (10,10),(5,5) and (0,5)

You need to find the area of the rectangle (0,10) (10,5) (0,5) and (5,5)

The lengths are 5, 5,5,5.

The area of the legs is = 5 × 5 =25

The area is;

$\rm Area =\dfrac{1}{2} \times \text{Distance between the parallel sides} \times \text{Sum of the parallel sides}\\\\Area =\dfrac{1}{2} \times 5 \times 5\\\\Area =12.5$

And the right triangle (10,5),(5,5), and (10,10) the right angle is at (10,5)

the two legs are lengths 5 and 5

so together they are 25 +12.5=37.5 square units.

Hence, the area of a trapezoid is bounded by the lines y = x, y = 10, y = 5, and the y− axis is 37.5 square units.

Learn more about trapezoids here;

brainly.com/question/15740528

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