A parallelogram has an area of 240 square inches and a height of 12 inches. What is the measurement of the base?

Mathematics

1 answer:

makvit [3.9K]3 years ago

7 0

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What is the distance (in units) between points C and D? Round your answer to the nearest hundredth.

r-ruslan [8.4K]

Given:

The two points on a coordinate plane are C(-5,-1) and D(0,3).

To find:

The distance between C and D.

Solution:

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using the distance formula, the distance between C(-5,-1) and D(0,3) is

$CD=\sqrt{(0-(-5))^2+(3-(-1))^2}$

$CD=\sqrt{(0+5)^2+(3+1)^2}$

$CD=\sqrt{(5)^2+(4)^2}$

$CD=\sqrt{25+16}$

On further simplification, we get

$CD=\sqrt{41}$

$CD=6.40312424$

$CD\approx 6.40$

Therefore, the distance between C and D is 6.40 units.

6 0

3 years ago

A triangular pennant has two sides that are 90 cm long each with an included angle of 25°.

Wittaler [7]

We are given with the following value:
AB = BC =90 cm
∠B =25°
∠D=90°

Solving the ∠C:
180 ° = (∠B/2) + ∠D +∠C
180° = (25°/2) + 90° + ∠C
180° - 12.5° -90° = ∠C
∠C = 77.5°

Solving for length in mD:
sin 77.5° = mD/90
mD = 90 sin77.5°
mD = 87.87

Solving for mDC:
cos 77.5 = mDC/90
mDC = 90 cos 77.5°
mDC = 19.48

Area = 1/2 * Base * Height
Area = 1/2 * 19.48*87.87
Area = 855.834

The total area of triangular pennant = 2 x 855.834 = 1,711.67 cm².

The area is 1,711.67 cm².