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2 years ago

Someone please solve for angle B

Mathematics

1 answer:

qaws [65]2 years ago

5 0

Answer:

<B=45°

Step-by-step explanation:

<A=<B (alternate angles)

5x-15=2x+21

5x-2x=21+15

3x=36

Dividing both sides by 3

x=12

Now

<A=5(12)-15

=60-15

=45°

<B=2(12)+21

=24+21

=45°

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2 years ago

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3 years ago

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dimulka [17.4K]

Answer:

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2 years ago

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by: