Question

Please help I need it for my study guide

Answer 1

40 ft²

Explanation:

First way:

A = 1/2bh = 1/2(16)(5) = 40

2nd way:

Length of dotted line at top = x

16² - 8² = x²

x² = 192

x = √192 = 13.86

Area rectangle = 8 x 13.86 = 110.85

Find the shaded area:

110.85 - 1/2(8)(13.86) - 1/2(8)(13.86 - 10) = 40

Answer 2

40 ft²

Explanation:

You want the area of a triangle two different ways. The height from the 10 ft base is given as 8 ft; the height from the 16 ft base is given as 5 ft.

Triangle area

The area formula for a triangle is ...

A = 1/2bh . . . . . . where b is the base, and h is the height from that base

Red

The base (side) dimensioned in red is 10 ft. The perpendicular distance to the opposite vertex is shown in red as 8 ft. Then the area is ...

A = 1/2(10 ft)(8 ft) = 40 ft²

Green

The base dimensioned in green is 16 ft. The perpendicular distance to the opposite vertex is shown in green as 5 ft. Then the area is ...

A = 1/2(16 ft)(5 ft) = 40 ft²

The area of the triangle is 40 ft².