Area Chapter 7

Area of Triangles and Parallelograms (7-1) Base of a triangle or parallelogram is any side. Altitude is the segment perpendicular to the base that goes to the vertex of the triangle or the opposite side of the parallelogram. Height is the measure of the altitude. Base of a triangle or parallelogram is any side. Altitude is the segment perpendicular to the base that goes to the vertex of the triangle or the opposite side of the parallelogram. Height is the measure of the altitude.

Area of Triangles and Parallelograms (7-1) Area of a triangle A = 1/2 bh Area of a parallelogram A = bh Area of a triangle A = 1/2 bh Area of a parallelogram A = bh

Area of Triangles (7-1) Find the area of triangle ABC.

Area of Triangles (7-1) If the area of a triangle is 32in 2, and one side of the triangle is 4in, what is the length of the corresponding altitude?

Area of Parallelograms (7-1) Find the area of the parallelogram.

Area of Parallelograms (7-1) Find the area of parallelogram EFGH with vertices E(-5, -3), F(-2, 3), G(2, 3), and H(-1, -3).

Area of Parallelograms (7-1) A parallelogram has 6-cm and 8-cm sides. The height corresponding to the 8-cm base is 4.5 cm. Find the height corresponding to the 6-cm base.

Pythagorean Theorem (7-2) In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a 2 + b 2 = c 2 In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. a 2 + b 2 = c 2 a b c

Pythagorean Theorem (7-2) Find the value of x. Leave your answer in simplest radical form.

Pythagorean Theorem (7-2) A right triangle has legs of length 16 and 30. Find the length of the hypotenuse.

Pythagorean Theorem (7-2) Pythagorean triples –3, 4, 5 –5, 12, 13 –8, 15, 17 –7, 24, 25 Pythagorean triples –3, 4, 5 –5, 12, 13 –8, 15, 17 –7, 24, 25

Pythagorean Theorem (7-2) Converse: If the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Pythagorean Theorem (7-2) If c 2 > a 2 + b 2, then the triangle is obtuse. If c 2 < a 2 + b 2, then the triangle is acute. If c 2 > a 2 + b 2, then the triangle is obtuse. If c 2 < a 2 + b 2, then the triangle is acute. a b c a b c

Pythagorean Theorem (7-2) A baseball diamond is a square with 90-ft sides. About how far is home plate from second base?

Pythagorean Theorem (7-2) The hypotenuse of an isosceles right triangle has length 20 cm. Find the area.

Pythagorean Theorem (7-2) Is the triangle a right triangle?

Pythagorean Theorem (7-2) The lengths of the sides of a triangle are given. Classify each triangle as acute, obtuse, or right. –15, 20, 25 –7, 8, 9 –12, 20, 13 The lengths of the sides of a triangle are given. Classify each triangle as acute, obtuse, or right. –15, 20, 25 –7, 8, 9 –12, 20, 13

Special Right Triangles (7-3) 45° - 45° - 90° –Both legs are congruent –The hypotenuse is √2 length of leg 45° - 45° - 90° –Both legs are congruent –The hypotenuse is √2 length of leg

Special Right Triangles (7-3) 30° - 60° - 90° –The hypotenuse is 2 shorter leg –The longer leg is √3 shorter leg 30° - 60° - 90° –The hypotenuse is 2 shorter leg –The longer leg is √3 shorter leg

Special Right Triangles (7-3) Find the length of the hypotenuse of a 45° - 45° - 90° triangle with legs of length 5√6.

Special Right Triangles (7-3) The longer leg of a 30° - 60° - 90° triangle has length 18. Find the lengths of the shorter leg and the hypotenuse.

Special Right Triangles (7-3) Find the value of each variable.

Special Right Triangles (7-3) A garden shaped like a rhombus has a perimeter of 100 ft and a 60° angle. Find the area of the garden to the nearest square foot.

Special Right Triangles (7-3) In quadrilateral ABCD, AD = DC and AC = 20. Find the area of ABCD. Leave your answer in simplest radical form.

Areas of Trapezoids, Rhombi, and Kites (7-4) Area of a trapezoid A = h (b 1 + b 2 ) –The height is the perpendicular distance between the bases. Area of a trapezoid A = h (b 1 + b 2 ) –The height is the perpendicular distance between the bases. 2

Areas of Trapezoids, Rhombi, and Kites (7-4) Area of a rhombus or kite A = 1/2 d 1 d 2 d - diagonals Area of a rhombus or kite A = 1/2 d 1 d 2 d - diagonals

Areas of Trapezoids, Rhombi, and Kites (7-4) Find the area of the trapezoid.

Areas of Trapezoids, Rhombi, and Kites (7-4) Find the area of trapezoid RQST.

Areas of Trapezoids, Rhombi, and Kites (7-4) Find the area of kite XYZW.

Areas of Trapezoids, Rhombi, and Kites (7-4) Find the area of kite ABCD and rhombus CDFE.

Areas of Regular Polygons (7-5) Regular polygon: –Interior angle sum = (n-2)x180 –Can be inscribed in a circle –Have a center and radius that are based on the circumscribed circle Area of a regular polygon A = 1/2 ap a - apothem - perpendicular distance from the center to a side p - perimeter Regular polygon: –Interior angle sum = (n-2)x180 –Can be inscribed in a circle –Have a center and radius that are based on the circumscribed circle Area of a regular polygon A = 1/2 ap a - apothem - perpendicular distance from the center to a side p - perimeter

Areas of Regular Polygons (7-5) Find the area of a regular 20-gon with 12-in. sides and a 37.9-in. apothem.

Areas of Regular Polygons (7-5) Find the area of the regular polygon. Round your answer to the nearest tenth.

Areas of Regular Polygons (7-5) Find the area of the regular polygon with the given radius. Leave your answer in simplest radical form.