##### 6-10.

*label*Mathematics

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6. **Area = 1/2 B * H = 1/2 (6)(4) = 24/2 = 12; Perimeter: 6 + 4 (SQRT 2) + 2 (SQRT 5),** If you cut the big triangle into two smaller right triangles, you get 2 base of left triangle, 4 base of right side triangle, and they share height of 4, then by Pythagorean theorem, left hypotenuse = 2^2 + 4^2 = c^2 = 4 + 16 = 20 = 4 (SQRT 5), and right hypotenuse is 4^2 + 4^2 = SQRT 32 = 2 (SQRT 5),

7. **Area = 1/2 B * H = 1/2 (3) (4) = 12/2 = 6: Perimeter: 3 +5 + 2 SQRT 3 = 8 + 2 SQRT 3,** By Pythagorean theorem, height = 4, base = 3 (of small right triangle), hypotenuse of small right triangle = 5, (which we only use to use Pythagorean theorem again on the obtuse angle where the base = 6, other side, 5 (which we just did by Pythagorean theorem) and larger side 2 (SQRT 3), 6^2 + 4^2 = 36 + 16 = SQRT 52 = 2 SQRT 3

8. Area = 1/2 B*H (right triangle) + Area of square (B*H) = 1/2 (3)(4) = 12/2 = 6 area of triangle left side, Area of square 4 * 4 = 16, so Total Area = 16 + 6 = **22**

**Perimeter: 7 + 4 + 4 + 5 = 20 (the two 4s are from the square, the 7 (base) and the 5 (hypotenuse of right triangle)**

9. Area of two right triangles (one on each end) + area square (middle), 1/2 (3) (3) = 9/2 (left right triangle) + 9 (3*3 = 9 for middle square) + 1/2 (1)(3) = 3/2** Total area = 9/2 + 9 + 3/2 = 12/2 + 18/2 = 30/2 = 15**

**Perimeter: 7 (total base length) + SQRT 13 (left hypotenuse of left right triangle) + 3 (top of square) + SQRT 10 (hypotenuse of right hand side right triangle) = 10 + SQRT 13 + SQR 10**

10. Area circle = PI R^2 = PI * 3^2 = **9(PI),** Perimeter of circle = circumference = 2* PI* R = 2 PI * 3 = **6 PI**

**If you wish you can estimate the square roots and PI, but if you want exact answer, keep the SQRT and PI as is. Estimate for PI is 3.1415**

**Best me if I explained it better and went through all of the steps. Let me know if you have any questions.**

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