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zheka24 [161]
3 years ago
6

Given: PSTK is a trapezoid, m∠P=90° SK =13, PK = 12, ST=8 Find: The area of PSTK.

Mathematics
1 answer:
guajiro [1.7K]3 years ago
5 0
<h3>Given</h3>

trapezoid PSTK with ∠P=90°, KS = 13, KP = 12, ST = 8

<h3>Find</h3>

the area of PSTK

<h3>Solution</h3>

It helps to draw a diagram.

∆ KPS is a right triangle with hypotenuse 13 and leg 12. Then the other leg (PS) is given by the Pythagorean theorem as

... KS² = PS² + KP²

... 13² = PS² + 12²

... PS = √(169 -144) = 5

This is the height of the trapezoid, which has bases 12 and 8. Then the area of the trapezoid is

... A = (1/2)(b1 +b2)h

... A = (1/2)(12 +8)·5

... A = 50

The area of trapezoid PSTK is 50 square units.

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